Determining method for lattice point for correspondence definition data creation and image processor

ABSTRACT

It used to be difficult to determine representative colors which allow color conversion with accuracy throughout color spaces without occurrences of local tone jump.  
     An ink quantity lattice point smoothness evaluation function for evaluating the smoothness of the disposition of ink quantity lattice points whose components are the ink quantities of inks in various colors and a CMY lattice point smoothness evaluation function for evaluating the smoothness of the disposition of CMY lattice points defined by CMY color components are defined. The CMY lattice points and the ink quantity lattice points wherein the ink quantity lattice point smoothness evaluation function and the CMY lattice point smoothness evaluation function are separately minimized are taken as lattice points for correspondence definition data creation. After both are separately substantially minimized, a binding condition is imposed so that the ink quantity lattices after readjustment will be converted into CMY color lattice points determined by the minimization by a predetermined transformation expression for converting ink quantity lattice points into CMY lattice points. Further, limitation on ink quantities adhering to a printing medium is imposed as a binding condition. Thus, the positions of the ink quantity lattice points are readjusted.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a determining method for latticepoints for correspondence definition data creation, an image processor,an image processing method, and a medium with an image processingprogram recorded thereon.

[0003] 2. Description of the Prior Art

[0004] Image devices, such as displays and printers, usually use colorimage data which renders the color of each pixel using specific colorcomponents with gradations. Colors are defined in various color spacesto obtain image data. Such color spaces include, for example, RGB colorspace and CMY-based color space. In the RGB color space, three colors, R(Red), G (Green), and B (Blue) are used. In the CMY-based color space, C(cyan)-based colors, M (magenta)-based colors, and Y (yellow)-basedcolors (including lc (light cyan, lm (light magenta), DY (dark yellow),and K (black)) are used. In general, these colors areequipment-independent colors which are specific to each image device.Therefore, to output the same images in the same colors with differentimage devices, LUTs (look-up tables) are used. LUTs define colorcorrespondence between devices.

[0005] It is unrealistic to define correspondence in LUT with respect toall the colors each image device can output because of storage capacity,workability in generating LUT, and the like. Usually, correspondence isdefined with respect to a specific number of representative colors, andcorrespondence is computed by interpolation with respect to any othercolor. That is, an immense number of colors are not subjected to colormeasuring. Instead, colors are outputted from image devices to theextent that color measuring is actually performable. Then, colormeasuring is performed to define LUTs with respect to a specific numberof representative colors.

[0006] To generate LUT, a specific number of these colors to besubjected to color measuring must be determined in advance. That is, aplurality of lattice points in color spaces must be determined. One ofconventional lattice point determining methods is color separation. Incolor separation, cubic lattice points are defined in the RGB space, forexample. Then, the RGB value of each lattice is subtracted form “255”,the maximum gradation value of each color, to obtain virtual CMY values.The number of 3 of CMY colors is not matched with the number of inks inprinting devices. Therefore, lattice points whose components are inkcolors are determined by defining a specific correspondence forconversion and converting the three colors into six colors or likemeans. Lattice point determining methods other than color separationinclude, for example, the art disclosed in Japanese Patent ApplicationNo. 2002-2061.

[0007] By the above-mentioned lattice point determining method, it isdifficult to determine representative colors wherewith color conversioncan be performed throughout color spaces with accuracy without localtone jump in gradations. More specific description will be given. Whencolor correspondence is computed using LUT, interpolation or the like isused as mentioned above. Therefore, with respect to colors other thanthe specific number of representative colors, color conversion accuracy,balance between colors (especially, gradations), and the like greatlydepend on how the specific number of representative colors are selected.However, in color separation mentioned above, such processing asconversion of three colors into six colors is performed according tosome sort of rule. Therefore, it is difficult to optimize lattice pointsthrough color spaces, taking various conditions into account on acase-by-case basis. Especially, with respect to printing devices,various conditions are imposed on specific colors. Such conditionsinclude limitation on ink quantity injectable into paper for printingand limitation on use of K ink for the prevention of grainy appearance.Therefore, it is very difficult to take various conditions locallyimposed into account and yet determine the lattice points ofrepresentative colors so that tone jump will not occur throughout.

SUMMARY OF THE INVENTION

[0008] The present invention has been made with the above-mentionedproblem taken into account. The present invention is intended to providea lattice point determining method for correspondence definition datacreation, an image processor, an image processing method, and a mediumwith an image processing program recorded thereon, wherein the latticepoints of representative colors which make tone jump less prone to occurthroughout color spaces.

[0009] According to a first aspect of the present invention, thefollowing is done to attain the above object: evaluation functions forevaluating the smoothness of lattice points are defined to determinelattice points which are referred to when correspondence definition datais created. The evaluation functions are substantially minimized, andthere by the positions of the lattice points are optimized. To determinethe lattice points of representative colors which make tone jump lessprone to occur throughout color spaces, a plurality of evaluationfunctions are individually substantially minimized. That is, withrespect to ink quantity lattice points whose components are color inkquantities, an ink quantity lattice point smoothness evaluation functionfor evaluating the smoothness of the disposition of the ink quantitylattice points is defined. With respect to CMY lattice points defined bythe respective color components of CMY, a CMY lattice point smoothnessevaluation function for evaluating the smoothness of the disposition ofthe CMY lattice points is defined. Then, the ink quantity lattice pointsmoothness evaluation function and the CMY lattice point smoothnessevaluation function are individually substantially minimized. Thesefunctions are so defined that the lower their values are, the morefavorable the smoothness of lattice points becomes. By minimizing thesefunctions, the positions of lattice point are optimized, that is, thesmoothness of lattice points becomes favorable.

[0010] At this time, the functions are individually minimized;therefore, the CMY lattice points and the ink quantity lattice pointsare separately optimized. The positions of the lattice points in the CMYcolor space and the positions of the lattice points in the color spacewhose components are ink colors are optimized in the respective colorspaces. Since these lattice points are optimized based on the separatefunctions, the lattice points in the individual color spaces cannot bebrought into one-to-one correspondence. After this optimization,however, the dispositions of the lattice points can be readjusted tobring them into certain correspondence. In that there is a possibilityof readjustment, each evaluation function only has to be substantiallyminimized in the above optimization. That is, even if the evaluationfunctions are not strictly minimized, there is no problem. Certaincorrespondence can be established between the lattice points in therespective color spaces, and further, positions close to lattice pointpositions wherein the evaluation functions are minimized can be adopted.This is done by computing minimal values to grasp the optimal positionsof lattice points in the respective color spaces and then makingreadjustment. As a result, correspondence definition data containingrepresentative color lattice points wherein tone jump is less prone tooccur can be determined.

[0011] As mentioned above, when separately optimized, the lattice pointsin the CMY color space and lattice points in the color space whosecomponents are ink colors do not correspond to each other. To cope withthis, the following is done in an in the aspect of the presentinvention: in the above optimization, each evaluation function issubstantially minimized, and then readjustment is made. In thisreadjustment, such binding conditions that ink quantity lattice pointsafter readjustment are converted into CMY color lattice pointsdetermined by the above minimization are imposed. Then, the ink quantitylattice points are moved. Thus, predetermined correspondence isestablished between the CMY lattice points and the ink quantity latticepoints.

[0012] In addition, in this readjustment, ink quantity limitation isimposed as a binding condition, and further, the ink quantity latticepoints are readjusted. The positions of the CMY lattice points and thepositions of ink quantity lattice points are optimized beforereadjustment. Therefore, by moving the ink quantity lattice points, theink quantity lattice points can be matched with the CMY lattice pointsas are optimized. Moreover, by reducing the movement of the ink quantitylattice points as much as possible, both the lattice points can bebrought into correspondence with each other, the ink quantity latticepoints also being substantially optimized. If ink quantity limitation isconsidered when the positions of the CMY lattice points and the inkquantity lattice points are optimized, it is very difficult to find theoptimal solution with all the conditions taken into account. Further,even if lattice points are determined by the found solution andcorrespondence definition data is created, it is difficult to preventthe occurrence of tone jump throughout the color gamut.

[0013] However, this can be coped with by the present invention.According to the present invention, CMY lattice points and ink quantitylattice points are optimized, and then ink quantity limitation isconsidered. Therefore, such a solution as to optimize both the latticepoints can be computed with ease regardless of ink quantity limitation.Furthermore, ink quantity limitation is considered in the end.Therefore, very realistic lattice points as lattice points for creatingcorrespondence definition data in a printing device can be determinedwith ease. With correspondence definition data created as the result,tone jump is less prone to occur, and highly accurate color conversioncan be performed.

[0014] When the above lattice points are determined, the individualevaluation functions need not be strictly minimized. Certaincorrespondence can be established between the lattice points in therespective color spaces, and further, positions close to lattice pointpositions wherein the evaluation functions are minimized can be adopted.This is done by computing minimal values to grasp the optimal positionsof lattice points in the respective color spaces and then makingreadjustment.

[0015] The correspondence definition data only has to be data whichdefines color correspondence used in a printing device and another imagedevice. For example, the data may be LUT or may be a so-called profilecontaining matrices which defines relations between colors. Inks used inprinting devices are usually CMY-based inks, and in a printing deviceaccording to the present invention, more color inks than three, CMY, canbe used. For example, four color inks in CMYK, six color inks inCMYKlclm, or more color inks can be used. In another image deviceaccording to the present invention, specific color components can beused to render various colors. For example, displays and the like whichuse the three colors of RGB as color components are possible.

[0016] RGB and CMY are so-called complementary colors to each other. Ifthese colors are rendered in 256 (0 to 255) shades of gray, it issupposed that C=255-R, M=255-G, and Y=255-B. This relation is notstrict. (Color matching by color measuring or the like is notperformed.) However, the lattice points in the RGB color space and thelattice points in the CMY color space can be brought into one-to-onecorrespondence. When lattices for correspondence definition datacreation are determined, lattice points in the CMY color space, not inthe RGB color space, may be used.

[0017] The colors defined as lattice points in the CMY color space areCMY-based colors. Therefore, the lattice points can be brought intocorrespondence with the quantities of inks which are similarly inCMY-based colors. For example, by multiplying vector whose elements aresix color inks by a 3×6 matrix, ink quantities can be brought intocolors in the CMY color space. Therefore, it can be concluded that: whenthe disposition of lattice points in the CMY color space is optimized bythe CMY lattice point smoothness evaluation function, the disposition oflattice points in the RGB color space is also optimized.

[0018] Lattice points in the CMY color space and lattice points in theink quantity color space can be brought into correspondence with eachother by a matrix or the like, as mentioned above. Therefore, in theabove-mentioned substantial minimization of evaluation functions, thefollowing processing can be performed: lattice points optimized ineither color space are fixed, and lattice points optimized in the othercolor space are readjusted. The number of ink colors is larger than 3 ofCMY. Therefore, the process of minimizing the ink quantity lattice pointsmoothness evaluation function is likely to give more solutions whichgive the minimum than the process of minimizing the CMY lattice pointsmoothness evaluation function does. If there are a large number ofsolutions, it is difficult to judge which solution is the optimalminimal value. In comparison, the optimal minimal value is easier tofind in minimal values of CMY lattice points. Consequently, thefollowing is preferably done: of optimized CMY lattice points and inkquantity lattice points, the CMY lattice points are fixed, and the abovebinding condition by matrix is imposed. Then, the disposition of inkquantity lattice points is readjusted.

[0019] The ink quantity lattice point smoothness evaluation function andthe CMY lattice point smoothness evaluation function only have to becapable of evaluating the smoothness of the disposition of latticepoints. Further, they only have to allow the positions of lattice pointsto be optimized by minimization of the functions. The smoothness ofdisposition is defined as the degree of skewness in the arrangement oflattice points arranged in a space. For example, if lattice points arearranged in cubic lattice shape in a three-dimensional space, there isno skewness. If lattice points are shifted from the cubic lattice pointpositions, skewness in the lattice is increased. Needless to add, thearrangement of lattice points need not be in cubic lattice shape. Statein which lattice points are arranged in specific positions in order isreferred to as state free from skewness. In this case, if skewness isincreased by deviation from the specific positions, the smoothness isdegraded. More specific description will be given. A sold formed by aplurality of lattice points will be considered. When parallel sides orparallel surfaces are reduced in number in the solid, skewness isconsidered to be increased. When parallel sides or parallel surfaces areincreased in number in the solid, the smoothness is considered to beincreased.

[0020] Here, a three-dimensional space has been taken as an example.Needless to add, in a color space whose color components are color inksused in a printing device, colors are defined in more than theedimensions because the number of color components is greater than 3 inthe space. In this color space as well, the smoothness can be defined onthe analogy of three-dimensional space. That is, if ink quantity latticepoints are arranged in specific lattice point positions in order (therelative positional relations between lattice points are substantiallyequal), the smoothness can be considered to be high. In general, thefollowing can be said with respect to interpolative calculation ofcolors positioned between lattice points in a color space: the moreorderly the lattice points are arranged, the better interpolation can beperformed without great variation in interpolating accuracy depending onlocal positions in the space. Therefore, according to the presentinvention, a specific number of the following lattice point positionscan be determined by optimizing the disposition of lattice points: thelattice point positions are where color measuring or the like isperformed when correspondence definition data is created and tone jumpis less prone to occur throughout the color space.

[0021] Further, the ink quantity lattice point smoothness evaluationfunction or the CMY lattice point smoothness evaluation function is notrequired to include only terms for evaluating the smoothness. That is,they are not required to include only terms whose value is increasedwhen the smoothness is degraded. In addition to the evaluation ofsmoothness, other various conditions may be added. Also, inreadjustment, a binding condition which adds ink quantity limitationonly has to be imposed, in addition to transformation expressions whichdefine the correspondence between CMY lattice points and ink quantitylattice points. Various limitations can be adopted as ink quantitylimitation. For example, in a printing device, various conditions areimposed on specific colors. Such conditions include limitation on inkquantity injectable into paper for printing and limitation on use of Kink for the prevention of grainy appearance. Consequently, theseconditions are incorporated into the evaluation functions. Morespecifically, terms whose value is increased with reduction in thedegree of accordance with conditions, such as ink quantity limitationand limitation on use of K ink, are incorporated. Thus, when thesmoothness of disposition of the above lattices is evaluated,optimization can be implemented with various binding conditions imposed.

[0022] According to a second aspect of the present invention, thefollowing is done when evaluation values in the smoothness evaluationfunction is enhanced to optimize the positions of lattice points: thedisposition of lattice points in a multi-dimensional color space and thedisposition of lattice points in a lower-dimensional color space areseparately optimized. After the optimization, the disposition of latticepoints in either color space is substantially maintained, and further,the disposition of lattice points in the other color space isreadjusted. Therefore, when the disposition of lattice points in eachcolor space is optimized, the optimization is not influenced by thedisposition of lattice points in the other color space. Thus, thedisposition can be made closer to the true optimal disposition in eachcolor space.

[0023] Further, according to a 10th aspect of the present invention, thedisposition cannot only be made closer to the true optimal dispositionin each color space. Also, ink quantity limitation can be reasonablyconsidered with the optimal disposition prevented from being disturbedas much as possible.

[0024] Here again, when the dispositions of lattice points in theindividual color spaces are separately optimized, they are optimizedwithout establishing any correlation between the respective positions.Therefore, the dispositions of lattice points cannot be directly broughtinto one-to-one correspondence to obtain lattice points forcorrespondence definition data creation. However, after thisoptimization, the disposition of lattice points is readjusted.Therefore, by considering their positional relation during thisreadjustment, certain relation can be established between them. Thus,lattice points for creating correspondence definition data which makethe lattice points in the two color spaces correspond to each other canbe determined.

[0025] Further, according to the 10th aspect of the present invention,ink quantity limitation is considered in readjustment. Therefore, highlyrealistic lattice points can be determined with ease as lattice pointsfor creating correspondence definition data in printing devices.Further, optimal solutions can be computed with ease because inkquantity limitation is not added when the above optimal positions oflattice points are determined. In readjustment, either of ink quantitylattice points and lower-dimensional color lattice points may be moved.In the present invention, however, it is preferable to move the inkquantity lattice points because ink quantity limitation is added. Thatis, when the ink quantity lattice points are moved, a binding conditionwherein the ink quantity limitation is formulated is imposed. With thisconstitution, the binding condition can be imposed, and further, the inkquantity lattice points can be readjusted.

[0026] The disposition of each lattice point is determined by enhancingthe smoothness of the disposition of lattice points. Therefore,correspondence definition data can be created by subjecting the colorindicated by the lattice point to color measuring or the like. Thereby,correspondence definition data containing representative color latticepoints which make tone jump less prone to occur can be determined.

[0027] At this time, the correspondence definition data only has to bedata which defines the correspondence between the ink quantity of eachcolor used in a printing device and the color component value of eachcolor used in another image device. Similarly to the above description,the data maybe LUT or may be also-called profile containing matriceswhich defines relations between colors. Further, as inks used in aprinting device, inks in four colors, CMYK, six colors, CMYKlclm, ormore colors can be used. Therefore, in the other image device, colorsonly have to be defined by a less number of color components, forexample, RGB, than the number of inks used in each printing device. Aplurality of lattice points determined according to the presentinvention are used when correspondence definition data is created. Forexample, when each color component value defined in LUT is determined,colors defined by color components of individual lattice points aresubjected to color measuring.

[0028] The ink quantity lattice point smoothness evaluation function andthe lower-dimensional color lattice point smoothness evaluation functiononly have to be capable of evaluating the smoothness of the dispositionof lattice points. Further, they only have to allow the positions oflattice points to be optimized by enhancing the evaluation values in thefunctions. Here again, the smoothness of disposition is defined as thedegree of skewness in the arrangement of lattice points arranged in aspace, as mentioned above. In general, the following can be said withrespect to interpolative calculation of colors positioned betweenlattice points in a color space: the more orderly the lattice points arearranged, the better interpolation can be performed without greatvariation in interpolating accuracy depending on local positions in thespace. Therefore, a specific number of the following lattice pointpositions can be determined by optimizing the lattice point positionsaccording to the present invention: the lattice point positions arewhere color measuring or the like is performed when correspondencedefinition data is created and tone jump is less prone to occurthroughout the color space.

[0029] Here again, needless to add, the ink quantity lattice pointsmoothness evaluation function or the lower-dimensional color latticepoint smoothness evaluation function is not required to include onlyterms for evaluating the smoothness. That is, they are not required toinclude only terms whose value is increased when the smoothness isdegraded. Similarly to the above description, in addition to theevaluation of smoothness, other various conditions may be added. In thissense, optimization according to the present invention is theoptimization of the positions of lattice points in individual colorspaces. These positions are such positions of lattice points that thesmoothness in the color space and other various conditions areconsidered and these are brought into favorable state from acomprehensive standpoint.

[0030] According to the present invention, the lower-dimensional colorspace only has to be a space defined by a smaller number of colorcomponents than the number of inks used in the above printing device.For example, when four or more color inks are used in a printing device,the CMY color space, the RGB color space, the Lab color space, or thelike can be adopted as the low-dimensional color space. (* is usuallyaffixed to L, a, and b, respectively but it is omitted in thisspecification for simplicity. This is the same with the followingdescription.) By enhancing evaluation in the ink quantity lattice pointsmoothness evaluation function and the lower-dimensional color latticepoint smoothness evaluation function, the dispositions can be separatelyoptimized. That is, the disposition of ink quantity lattice points andthe disposition of lower-dimensional color lattice points can beseparately optimized. Therefore, optimal positions can be individuallydetermined without the constraint of the other's lattice pointpositions.

[0031] After this optimization, either optimized lattice points aremaintained, and further, the other optimized lattice points arereadjusted. Therefore, it is possible to keep the lattice points in atleast either color space optimized and determine favorable latticepoints in the other color space as well. Similarly to the abovedescription, the readjustment can be made as follows: a matrix or thelike which brings the lower-dimensional color lattice points and the inkquantity lattice points into correspondence with each other is defined.Thus, the relation between both the lattice points is maintained by thematrix. Then, the positions of the other lattice points are readjusted.Needless to add, there are cases wherewith either of a plurality oflattice points fixed, the other cannot be optimized. In such cases, itis not strictly required to fix either lattice points. That is, it isunnecessary to fix either with respect to all the lattice points. Withrespect to some lattice points, readjustment may be made with themovement thereof reduced as much as possible.

[0032] Further, according to the 10th aspect of the present invention,this readjustment is made so that ink quantity limitation will be met.

[0033] As mentioned above, the positions of lattice points are optimizedby enhancing evaluation in the ink quantity lattice point smoothnessevaluation function and the lower-dimensional color lattice pointsmoothness evaluation function. This constitution can be implemented invarious ways. A third aspect of the present invention is so constitutedthat: the values of evaluation functions are increased with increase inthe difference between the relative positional relation between twoadjacent lattice points and the relative positional relation betweenother two adjacent lattice points. As a result, the optimal latticepoint can be searched by minimizing these evaluation functions.

[0034] A fourth aspect of the present invention is another perfectexample of the constitution wherein the difference between the relativepositional relation between two lattice points and the relativepositional relation between other two lattice points is considered.According to this aspect, two vectors are considered: one is the vectorbetween adjacent lattice points containing a lattice point of interest.The other is the vector between adjacent lattice points containing acomparative lattice point. Then, the value obtained by dividing thedifferential vector between both the vectors by the distance between thelattice point of interest and the comparative lattice point is includedin the components of the evaluation functions. In consideration of theoperation of minimizing evaluation functions, the evaluation functionsare preferably scalar functions. Therefore, such constitution that thiscomponent is raised to the second power or absolute values are usedshould be adopted. Further, by dividing the above differential vector bythe distance between the lattice point of interest and the comparativelattice point, the smoothness of lattice point disposition can bestandardized and incorporated into the functions. That is, when thedistance between the lattice point of interest and the comparativelattice point is great, the difference in the relative positionalrelation to lattice points adjacent to these lattice points is supposedto be great. Therefore, the difference in relative positional relationis qualitatively incorporated into the evaluation functions by dividingthe differential vector by the distance between the lattice point ofinterest and the comparative lattice point. As a result, the dispositionof lattice points can be optimized by minimization of the evaluationfunctions.

[0035] As mentioned above, terms other than those for evaluating thesmoothness of lattice point disposition can be incorporated into the inkquantity lattice point smoothness evaluation function and thelower-dimensional color lattice point smoothness evaluation function. Afifth aspect of the present invention is one example of thisconstitution. According to this aspect, a function whose value isincreased as the lattice point of interest gets away from a specificposition is included in the evaluation functions. With such anevaluation function, the lattice point of interest can be prevented fromdrastically moving from the specific position in the process ofminimization of the evaluation function. In the process of minimization,the lattice point of interest is moved as appropriate. If this movingdistance is great, the evaluation functions oscillate or diverge, and itis often difficult to converge them in the minimal value. To cope withthis, measures are taken so that the farther the lattice point ofinterest gets away from a specific position, the more the values ofevaluation functions are increased. Thus, a binding condition can beimposed so as to prevent the lattice point from drastically moving fromthe specific position.

[0036] Meanwhile, by defining the specific position based on variousintentions, a binding condition reflecting the various intentions can beobtained. As an example, a case where the position of the lattice pointof interest is shifted to minimize the evaluation functions andcomputation is performed to repeat this process of minimization by aplurality of times will be considered. In this case, the drasticmovement of the lattice point of interest can be prevented by taking theposition of the lattice point before movement as the specific position.If it is desired to impose such a condition as to prevent reduction inthe color saturation of a color indicated by a lattice point in theprocess of minimization, there is no problem. The position whichindicates the color equivalent to the color saturation of the colorindicated by the position of the lattice point of interest is taken asthe specific position. Thus, such a binding condition as to prevent thecolor saturation from being unnecessarily reduced can be imposed. Forthis binding condition, various conditions can be imposed. A bindingcondition based on the same intention may be imposed both on the inkquantity lattice point smoothness evaluation function and on thelower-dimensional color lattice point smoothness evaluation function.Or, binding conditions based on different intentions may be imposed.

[0037] A sixth aspect of the present invention is a concrete example ofthe constitution wherein a binding condition is imposed on evaluationfunctions. According to this aspect, a function whose value is increasedas the color indicated by the lattice point of interest departs from aspecific color is included in the evaluation functions. More specificdescription will be given. Each lattice point indicates a specific colorin each color space. If minimizing evaluation functions is onlyconsidered, lattice point positions are shifted without reflecting thefeatures of the color of each lattice point, and this results in changein colors. Needless to add, according to the present invention, latticepoint positions are optimized while colors subtly are changed. Withrespect to some colors, it is unfavorable to freely shit lattice pointpositions to freely vary colors.

[0038] One example of such cases is lattice points which render gray bythe three color components of CMY being substantially equivalent. Withrespect to such lattice points, if a specific color component isfluctuated just because evaluation functions are minimized, the colorcan depart from gray. In some cases, it is desired to store colorcomponent “0” with respect to a color wherein any one or two of threecolor components of CMY are “0.” In these cases, such constitution thatthe evaluation functions are increased as the color indicated by eachlattice point departs from a specific color can be adopted. Thus, it ispossible to prevent the color from largely departing from the specificcolor and further optimize lattice point positions.

[0039] Further, there are cases where the color indicated by a latticepoint is identified by a coordinate value which identifies the positionof the lattice point; and furthermore, such a coordinate system thatcoordinate values cannot be negative in a color space is adopted. Inthis case, a function whose value is increased with increase in theabsolute value of coordinate values, which are negative, is preferablyincluded in the evaluation functions. However, in case of a functionwhose value is increased as the lattice point of interest gets away froma specific position, as mentioned above, the following conditions can beimposed: conditions practically equivalent to a function whose value isincreased with increase in the absolute value of a coordinate value,which is negative. Needless to add, if the range of coordinates islimited in each coordinate system, the maximum value can exist in eachcoordinate value. Therefore, it is possible to include such a conditionthat the maximum value will not be exceeded in the evaluation functions.Here again, in case of a function whose value is increased as thelattice point gets away from a specific position, the followingconditions can be imposed: conditions practically equivalent to afunction whose value is increased as the coordinate value fartherexceeds the maximum value of that coordinate system.

[0040] Various algorithms can be adopted for minimizing evaluationfunctions as mentioned above. One of perfect examples of thisconstitution is a seventh aspect of the present invention. According tothis aspect, evaluation functions have color components constitutingindividual color spaces as variables. Therefore, by varying the valuesof the variables and further searching the minimal values of theevaluation functions, color component values as are minimized can becomputed. As a result, lattice point positions in the minimized statecan be determined.

[0041] When the evaluation of the smoothness of lattice pointdispositions indicated by evaluation functions is enhanced, some latticepoint position is shifted to search a position wherein the evaluationfunctions are minimized. According to the present invention, a deviationis added to each color component, and the lattice point is therebyconsidered to have been moved. Further, it is considered that theevaluation functions have been minimized with the deviation added. Thus,for example, by partially differentiating the evaluation function byeach color component to compute the minimal value, a deviation whichminimizes the evaluation function can be computed. By repeating thisprocessing, the position of a lattice point converges in the optimalposition, and thus the evaluation of the smoothness of disposition canbe enhanced. Needless to add, according to the present invention, allthe lattice points can be determined by repeating the same processingwith respect to each lattice point. This is because according to thepresent invention, a plurality of lattice point positions are determinedin color spaces.

[0042] Further, in minimization of evaluation functions, other variousalgorithms can be adopted. The following technique may be adopted: in anevaluation function which has each color component constituting a colorspace as a variable, the evaluation function is partially differentiatedby each color component. Further, a color component which zeroes thepartial differentiation value is computed. However, the above-mentionedtechnique to utilize deviations to determine lattice point positions hasan advantage of enhanced convergeability. That is, by multiplying adeviation by a coefficient having a value of 0 to 1, the magnitude ofthe deviation can be adjusted, and the positions of lattice points areprevented from drastically shifting. As a result, in the above-mentionedprocess of minimization, evaluation functions can be prevented fromoscillating or diverging. They can be made to promptly converge in theminimal value.

[0043] The above-mentioned lower-dimensional color space is smaller innumber of color components than the ink quantity space. Therefore, inthe lower-dimensional color space, it is easier to find the minimalvalues of evaluation functions. Since minimal values are easy to find,the following is preferably done in the above-mentioned readjustment:lattice points in the lower-dimensional color space are maintained, andlattice points in the ink quantity space are readjusted. When thisconstitution is adopted, it can be taken into account that latticepoints in the ink quantity space are readjusted. Thus, theabove-mentioned minimization utilizing deviations may be applied only tooptimization of the positions of lattice points in the lower-dimensionalcolor space.

[0044] According to the present invention, either of optimized inkquantity lattice points and lower-dimensional lattice points ismaintained, and the other is readjusted. Thereby, the above-mentionedcorrespondence definition data wherein the optimized lattice points arecontained, and further, the lower-dimensional lattice points and the inkquantity lattice points are in correspondence with each other iscreated. A perfect example of the constitution for this purpose is aneighth aspect of the present invention. According to this aspect, theabove-mentioned lower-dimensional color lattice points are substantiallymaintained, and further, the ink quantity lattice points are readjusted.Further, when readjustment is made, a binding condition is imposed sothat both the lattice points can be brought into correspondence witheach other by a predetermined transformation expression. Therefore,lattice points independently optimized by separate evaluation functionsare provided with predetermined correspondence after readjustment.Though color matching, such as color measuring, is not performed,correspondence definition data wherein colors in both the color spacesare in correspondence with each other and optimally disposed latticepoints are contained can be determined.

[0045] At this time, various transformation expressions can be adoptedfor the predetermined transformation expression. For example, matricescan be adopted. A case where the number of ink colors is 6 and the colorcomponents in the lower-dimensional color space are in three colors willbe considered. In this case, the ink quantity lattice points can beconverted into the lower-dimensional color lattice points by convertingsix colors into the three colors by a 3×6 matrix. With respect totransformation expressions, conversion from multiple dimensions intolower dimensions is preferable because univocal relation can be moreeasily defined by this conversion. More specific description will begiven. When a color is identified in the lower-dimensional color space,there are many lattice points indicating substantially the same color inthe multi-dimensional color space. However, if a color is identified inthe multi-dimensional color space, there is usually only one latticepoint indicating substantially the same color in the lower-dimensionalcolor space. In this case, the matrix can be determined with ease.

[0046] Further, a case where the above-mentioned readjustment with abinding condition imposed will be considered. Similarly to theabove-mentioned description, there are cases where it is unfavorable tomaintain the positions of lower-dimensional color lattice points withconformity with various conditions taken into account. In such cases aswell, it is not indispensable to maintain the positions oflower-dimensional color lattice points. That is, lower-dimensional colorlattice points can be fixed as much as possible, and further, thepositions of ink quantity lattice points can be moved.

[0047] An 11th aspect of the present invention is a perfect example ofthe constitution related to the above-readjustment. According to thisaspect, a first movement evaluation function is defined. This functionincludes a function whose value is increased with increase in thedistance between the readjusted lattice point and the other optimizedlattice point. That is, by minimizing this first movement evaluationfunction, the movement can be reduced as much as possible when the otheroptimized lattice point is readjusted. As a result, such lattice pointpositions as described below can be determined: lattice point positionswherein the movement of optimized lattice points is reduced as much aspossible; predetermined correspondence can be provided between inkquantity lattice points and lower-dimensional color lattice points; andfurther, ink quantity limitation is also taken into account.

[0048] Various conditions to be considered when ink is made to adhere toa printing medium can be taken into account as ink quantity limitation.One of examples of the constitution is a 12th aspect of the presentinvention. According to this aspect, limitation on the maximum quantityof ink adhering to a specific printing area is taken into account whenthe above-mentioned readjustment is made. More specific description willbe given. If ink is excessively made to adhere to a printing medium,troubles, such as ink's flowing after printing, occur. Therefore, ingeneral, the quantity of ink which can be made to adhere to a specificarea is limited. Consequently, the above-mentioned other optimizedlattice points are moved with this limitation taken into account. Thus,lattice point positions with ink quantity limitation also taken intoaccount can be determined.

[0049] As a result, with correspondence definition data eventuallycreated, such color conversion that inks are discharged against inkquantity limitation can be prevented from being carried out. At thistime, limitation on the quantity of link adhering to a printing mediumonly has to be taken as a condition. Various areas can be adopted as theabove specific printing area. If limitation is imposed on ink quantitydischarged per pixel in image data, for example, the area equivalent toone pixel corresponds to the specific area.

[0050] Various constitutions can be adopted as the concrete constitutionfor defining the maximum quantity of ink adhering. One example of suchconstitutions is a 13th aspect of the present invention. According tothis aspect, computation is made by adding the product of a weightingfactor whose value is “0” or “1” defined for each ink quantity componentvalue and each component value of the ink quantity lattice points. Morespecific description will be given. By adding an ink quantity defined byeach component value at each ink quantity lattice point, the quantity ofink consumed for a certain pixel can be determined. However, processingrelated to the present invention is preferably automatized by acomputer. In this case, conditions are preferably described by auniversal method which can express all the cases.

[0051] Accordingly, an ink quantity is determined by multiplication of acoefficient which can take “0” or “1” as a weighting factor by an inkquantity component value, and the ink quantity is thereby formulated.Thus, with respect to a combination of arbitrary ink quantity componentvalues, a condition can be defined with ease. If a condition isformulated, the first movement evaluation function can be easilyminimized with the ink quantity limitation taken into account by takingthe conditional expression as a binding condition.

[0052] Further, another limitation can be imposed on ink quantity as ina 14th aspect of the present invention. According to this aspect,limitation is imposed on the quantity of specific color ink consumed ata specific gradation value. More specific description will be given. Ifa specific color ink is used for a specific color, the drops of thespecific color ink can be conspicuous in the print result, which cangive grainy appearance. To cope with this, limitation is imposed on useof the specific color ink in some cases. For example, if high-density Kink is used when light colors are used to render colors of highlightness, that is prone to give grainy appearance.

[0053] In this case, by imposing limitation to prevent use of K ink forspecific colors, the production of grainy appearance can be prevented.Achromatic colors rendered by K ink can be alternatively rendered by acombination of CMY inks or other means. Therefore, the constitution withlimitation on K ink is especially favorable.

[0054] Various constitutions can be adopted as a concrete constitutionfor defining limitation on the quantity of specific color ink consumed.One example of such constitutions is a 15th aspect of the presentinvention. According to this aspect, the limitation is imposed oncondition that the product of a weighting factor whose value is “0” or“1” defined for each ink quantity component value and each componentvalue of the ink quantity lattice points is zeroed. More specificdescription will be given. When the weighting factor which takes thevalue of “0” or “1” is multiplied by an ink quantity component value,the result takes the value of “0” or another value. To limit use of aspecific color ink, the value of that ink quantity color componentshould be “0” or a value close thereto. To impose a condition that theink quantity component value is zeroed, “1” can be taken as theweighting factor for the ink quantity component value. This is because,to satisfy the condition that the above product is zero, the inkquantity component value must be “0.”

[0055] Processing related to the present invention is preferablyautomatized by a computer. Thus, conditions can be described by auniversal method whereby all the cases can be expressed by defining acondition as mentioned above. Therefore, the automatization by computeris favorable. By formulating conditions as mentioned above, the firstmovement evaluation function can be easily minimized with ink quantitylimitation taken into account.

[0056] In readjustment, either of optimized lattice points ismaintained, and the other optimized lattice point positions are moved asa rule. However, there are cases where, because either of the optimizedlattice points is maintained, the other optimized lattice pointpositions cannot be converged. In such cases, maintaining either latticepoint positions is not always indispensable, and such a constitution asaccording to a 16th aspect of the present invention is possible. Morespecific description will be given. There are cases where, when eitherof optimized lattice point positions is maintained, a solution whichminimizes the first movement evaluation function does not exist. In suchcases, shifting of the positions of the either optimized lattice pointsis permitted.

[0057] Further, a second movement evaluation function is defined. Thesecond movement evaluation function includes a function whose value isincreased with increase in the distance between the readjusted latticepoint and the other optimized lattice point and further increased withincrease in the moving distance of the either optimized lattice point.If the second movement evaluation function is minimized with thisconstitution, the either optimized lattice point is also moved.Therefore, a lattice point position wherein the position of the otheroptimized lattice point does not diverge or oscillate and the evaluationfunction converges in the minimal value can be determined.

[0058] One example of constitutions suitable for defining the secondmovement evaluation function is a 17th aspect of the present invention.More specific description will be given. There are cases where it isundesired to freely move both the either optimized lattice point and theother optimized lattice point by the same movement. An example is a casewhere it is desired to maintain the positions of the either optimizedlattice points as much as possible. In this case, the likelihood ofmoving of both the lattice points can be controlled by taking thefollowing measure: a function is defined so that the unit fluctuation ofthe either optimized lattice point more greatly contributes to increasein the value of the second movement evaluation function than the unitfluctuation of the other optimized lattice point.

[0059] More specific description will be given. The fluctuations of boththe lattice points increase the value of the second movement evaluationfunction. Therefore, when the second movement evaluation function isminimized, the lattice points are moved so that the amounts offluctuations of both the lattice points will be reduced as much aspossible. If either's contribution and the other's contribution aredifferent from each other, one that makes a greater contribution morelargely increases the second movement evaluation function by slightfluctuation. Therefore, in the process of minimizing the second movementevaluation function, the movement is conversely suppressed.

[0060] Various constitutions can be adopted to adjust contribution ofeach lattice point making unit fluctuation. One example of theconstitutions is such that a term comprising the difference between thevector before moving and the vector after moving of each lattice pointand a weighting factor is incorporated into the second movementevaluation function. This constitution is created so that the weightingfactor for vector difference with respect to either optimized latticepoint will have a greater absolute value.

[0061] Another example of constitutions suitable for defining the secondmovement evaluation function is an 18th aspect of the present invention.More specific description will be given. There are cases where it isundesired to allow the color corresponding to the lattice point ofinterest to be greatly fluctuated by fluctuation in the component valuesof individual lattice points. When the component values of individuallattice points are compared, the magnitude of the absolute values ofcomponent values is disregarded with respect to the second movementevaluation function. Then, contribution at the same level is giventhereto. Thus, the likelihood of moving of each component is brought tothe same level. However, even in case of the same amount of fluctuation,component values having a small absolute value and those having a largeabsolute value are different in their influences on colors. The unitfluctuation of component values having a small absolute value hasgreater influences on colors.

[0062] Accordingly, components having a small absolute value are soconstituted that they make a relatively great contribution to the valueof the second movement evaluation function as compared with componentshaving a large absolute value. As a result, the degrees of fluctuationin colors indicated by individual lattice point caused by fluctuation ofindividual component values can be averaged. Further, the influencesexercised on colors by fluctuation of individual components can beaveraged, and further, the second movement evaluation function can beminimized. Various constitutions can be adopted to relatively change thedegree of contribution of each component. For example, a term obtainedby multiplying each component of the either optimized lattice points bya weighting factor is incorporated in the second movement evaluationfunction. Further, such a constitution that the weighting factors ofindividual components are the reciprocal numbers of respective componentvalues. Thus, contribution from each component can be uniformized.

[0063] Once lattice points for correspondence definition data creationare determined, colors outputted by a printer in ink quantitiesdetermined by the lattice points for correspondence definition datacreation can be subjected to color measuring. Further, the inkquantities can be brought into correspondence with colors used inanother image device by that color measuring value. As a result, LUTsand profiles which make tone jump less prone to occur throughout colorspaces can be created. When colors used an image device other thanprinters are converted into ink quantities which define colors used inthe printer, these LUTs or profiles can be used. Thus, color conversioncan be carried out throughout color spaces without the occurrence oftone jump.

[0064] Therefore, it can be said that processors and the like utilizingthese LUTs or profiles utilize the technical philosophy of the presentinvention. More specifically, the present invention remains effective asa substantive image processor like a 19th or 22nd aspect of the presentinvention. The present invention is also effective as a substantiveimage processing method like a 20th or 23rd aspect of the presentinvention. Such an image processor or image processing method can besolely implemented, or can be incorporated into some equipment andimplemented together with another apparatus or method. Thus, thephilosophy of the present invention is not limited to these aspects butcan be implemented in various embodiments. The embodiments of thepresent invention can be modified as appropriate, and the presentinvention may be embodied in software or in hardware.

[0065] If the philosophy of the present invention is embodied insoftware for implementing an image processor or image processing method,the philosophy of course exists on a recording medium with such softwarerecorded thereon. The philosophy is utilized in such a form. Therefore,the present invention can be embodied as a medium with an imageprocessing program recorded thereon like a 21st or 24th aspect of thepresent invention. Needless to add, the recording medium may be amagnetic recording medium or a magneto-optic recording medium, and thisis the same with any recording medium that will be developed in thefuture. Also, this is completely the same with the phases ofreproduction, such as primary duplicate copies and secondary duplicatecopies, completely without question.

[0066] Even if a communication line is used as a method for supply,there is no difference in that the present invention is utilized. If thepresent invention is embodied partly in software and partly in hardware,that is completely the same in the philosophy of invention. Such anembodiment that part of the program is stored on a recording medium andread in as required may be adopted. Or, all the functions need notnecessarily be implemented in the program itself, but some functions maybe implemented by an external program or the like. This is because evenin this case, every function only has to be capable of being implementedby a computer. The above-mentioned lattice point determining method forcorrespondence definition data creation holds as an invention.Therefore, needles to add, apparatuses and programs for implementing themethod also hold as the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0067]FIG. 1 is a functional block diagram of a color correction LUTgenerator.

[0068]FIG. 2 is a block diagram schematically illustrating an example ofthe hardware configuration of the color correction LUT generator and theimage processor.

[0069]FIG. 3 is a functional block diagram of the image processor.

[0070]FIG. 4 is a flowchart illustrating color conversion processing.

[0071]FIG. 5 is a flowchart schematically illustrating the processing inthe color correction LUT generator.

[0072]FIG. 6 is a flowchart illustrating the processing to compute CMYlattice points.

[0073]FIG. 7 is a drawing illustrating the positional relation betweenCMY lattice points.

[0074]FIG. 8 is a drawing illustrating the positional relation betweenink quantity lattice points.

[0075]FIG. 9 is a flowchart illustrating readjustment processing.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0076] Here, embodiments of the present invention will be described inthe following order:

[0077] (1) Constitution of the Present Invention:

[0078] (2) Image Processor:

[0079] (3) Image Processing Control Program:

[0080] (4) Color Correction LUT Generator:

[0081] (5) Optimization by CMY Lattice Point Evaluation Function:

[0082] (5-1) Cost Estpn:

[0083] (5-2) Cost Esopn:

[0084] (5-3) Cost Esapn:

[0085] (5-4) Computation of Vector Which Gives Minimal Value:

[0086] (6) Optimization by Ink Quantity Lattice Point EvaluationFunction:

[0087] (6-1) Cost Eitpn:

[0088] (6-2) Cost Eiopn:

[0089] (6-3) Computation of Vector Which Gives Minimal Value:

[0090] (7) Readjustment Processing:

[0091] (8) Other Embodiments:

[0092] (1) Constitution of the Present Invention:

[0093]FIG. 1 is a functional block diagram of a color correction LUTgenerator. The generator utilizes the lattice point determining methodfor correspondence definition data creation in an embodiment of thepresent invention to generate color correction LUTs. The colorcorrection LUT generator 20A illustrated in the figure performs colormeasuring on colors indicated by lattice points for correspondencedefinition data creation determined by the lattice point determiningmethod for correspondence definition data creation of the presentinvention. Then, the generator 20A determines correspondence betweensRGB data and CMYKlclm data based on the color measuring values. Thethus determined correspondence is defined in color correction LUTs,which are utilized when color conversion is carried out in imageprocessing.

[0094]FIG. 3 is a functional block diagram of the image processor in theembodiment of the present invention. That is, the image processor is adevice for carrying out color conversion using color correction LUTsgenerated by the color correction LUT generator 20A. FIG. 2 is a blockdiagram schematically illustrating an example of the hardwareconfiguration of the color correction LUT generator and the imageprocessor. In this embodiment, a computer system is adopted as anexample of hardware which embodies the color correction LUT generatorand the image processor.

[0095]FIG. 2 illustrates this computer system in the form of blockdiagram. The computer system comprises a scanner 11 a, a digital stillcamera 11 b, and a video camera 11 c as image input devices, which areconnected with a main unit 12. These input devices are capable ofdisplaying image data, which represents images in a dot (pixel) matrix,in 256 shades of gray in three primary colors of RGB. The input devicesare respectively capable of thereby rendering approximately 16.7 millioncolors.

[0096] The main unit 12 is connected with a flexible disk drive 13 a, ahard disk 13 b, and a CD-ROM drive 13C as external auxiliary storages.Major programs related to the system are recorded on the hard disk 13 b,and required programs and the like can be read out of a flexible disk,CD-ROM, or the like as required. In addition, the main unit 12 isconnected with a modem 14 a as a communication device for connecting themain unit to an external network or the like. When the main unit 12 isconnected to an external network through a public network, software anddata can be downloaded and introduced therein. In this example, thecomputer system is so constituted that external access is made overtelephone line by the modem 14 a. However, such a constitution thataccess to a network is made through a LAN adaptor can be adopted. Inaddition to the forgoing, a keyboard 15 a and a mouse 15 b are connectedfor operating the main unit 12.

[0097] Further, the computer system comprises a display 17 a, a colorprinter 17 b, and a projector 17 c as image output devices. The display17 a is provided with a display area of 800 pixels in the horizontaldirection by 600 pixels in the vertical direction. The display 17 iscapable of displaying the above-mentioned 16.7 million colors at eachpixel. This resolution is illustrative only, and may be modified to640×480 pixels, 1024×768 pixels, or the like as appropriate.

[0098] The color printer 17 b is an ink jet printer, and is capable ofjetting dots onto paper for printing as media using six color inks ofCMYKlclm and thereby printing images. With respect to pixel density, theprinter 17 b is capable of performing as high-density printing as360×360 dpi or 720×720 dpi. However, with respect to rendering withgradation, the printer 17 b prints images in two shades of gray, thatis, based on whether to apply color ink or not. While an image isinputted using such an image input device, it is displayed on oroutputted to an image output device. Therefore, predetermined programsare executed in the main unit 12.

[0099] Of these programs, an operating system (OS) 12 a runs as theprimary program. The operating system 12 a has various drivers builttherein: a display driver 12 b which causes the display 17 a to displayimages; a printer driver 12 c which causes the color printer 17 b toproduce printout; and a projector driver 12 i (not shown) which causesthe projector l7 c to produce a display. These drivers 12 b, 12 c, and12 i depend on the kind of the display 17 a, the color printer 17 b, andthe projector 17 c, and can be added to the operating system 12 aaccording to the respective kind. Further, the drivers are capable ofcarrying out additional functions above the standard in dependence onthe kind of equipment. That is, a common processing system can bemaintained on the standard system of the operating system 12 a, andvaried processing can be additionally carried out within the allowablerange.

[0100] As the basis for executing these programs, the main unit 12comprises CPU 12 e, RAM 12 f, ROM 12 g, I/O 12 h, and the like. The CPU12 e which performs computation uses the RAM 12 f as a temporary workarea, setting storage area, or program area, and further, executes theprimary program written in the RAM 12 f as appropriate. Thus, the CPU 12e controls external or internal equipment connected through the I/O 12h.

[0101] At this time, applications 12 d are executed on the operatingsystem 12 a as the primary program. The details of processing performedby applications 12 d vary from one application to another. For example,some monitors the operation of the keyboard 15 a or the mouse 15 b as anoperating device. When these operating devices are operated, someappropriately controls varied external equipment and performscorresponding processing. Further, some displays the result ofprocessing on the display 17 a or outputs it to the color printer 17 b.

[0102] In such a computer system, image data can be acquired by thescanner 11 a or the like as an image input device, and it can besubjected to predetermine image processing by applications 12 d. Then,the result of processing can be displayed on or outputted to the display17 a, the color printer 17 b, or the projector 17 c as an image outputdevice.

[0103] In this embodiment, the image processor is implemented as acomputer system. However, such a computer system is not always required.The image processor only has to be a system which is capable ofsubjecting similar image data to image processing according to thepresent invention. For example, such a system that an image processorwhich performs image processing according to the present invention isbuilt in a digital still camera is acceptable. In this case, a colorprinter is caused to produce printout using the processed image data.

[0104] Further, a color printer which is fed with image data withoutintervention of a computer system and prints it may be so constitutedthat: image data inputted through a scanner, a digital still camera, amodem, or the like is automatically subjected to image processingaccording to the present invention, and then printing processing isperformed. In addition, the present invention is of course applicable tovaried equipment, such as a color facsimile machine, a color copymachine, and a projector, which handles image data.

[0105] (2) Image Processor:

[0106] Next, processing performed when the computer system 12 is causedto function as an image processor of the present invention will bedescribed. In the computer system 12, the input images of the scanner 11a, the digital still camera 11 b, and the video camera 11 c and theoutput images of the display 17 a and the projector 17 c can be printedon the printer 17 b. In this image printing, processing utilizing colorcorrection LUTs is performed.

[0107] More specific description will be given. It is assumed that thesame image is handled on different image devices, for example, on animage input device and on an image output device. If in image data usedin the respective image devices, the colors at individual pixels arerendered in different color spaces, color conversion is carried outreferring to color correction LUTs. At this time, color correction LUTsgenerated by the color correction LUT generator 20A are referred to. Inthis embodiment, the image input devices, the display 17 a, and theprojector 17 c use sRGB data, and the printer 17 b uses CMYKlclm data.Both types of data are brought into correspondence with each other byreferring to color correction LUTs. According to this embodiment, thisprocessing is performed by the printer driver 12 c. In other words, thecomputer system 12 on which the printer driver 12 c is executedfunctions as an image processor according to the present invention.

[0108] In FIG. 3, the image processor 20B subjects sRGB image input datato color conversion processing, and outputs CMYKlclm image output dataas an output image signal. Each image data is obtained bycolor-separating color images into predetermined color components, andindicates the intensity of each color component. Individual colorcomponents are chromatic colors, and render an achromatic color,typified by gray, black, or white when mixed at a predetermined ratio.

[0109] The image processor 20B comprises a color correction LUT storingportion 20 b which, at least, stores color correction LUTs generated bythe color correction LUT generator 20A; and a color correcting portion20 a which reads a color correction LUT selected by a color correctionLUT selecting portion 20 c out of the color correction LUT storingportion 20 b and converts sRGB data into CMYKlclm data referring to thecolor correction LUT read out. Provided with this configuration, theimage processor 20B performs the above-mentioned color conversionprocessing in accordance with the flow illustrated in FIG. 4. The useris supposed to operate the keyboard 15 a or the like to give aninstruction to print the image. In response to the instruction, imageoutput is stated (Step 70).

[0110] When image output is started, a predetermined color correctionLUT to be referred to when the image of interest is printed is selected.That is, a plurality of color correction LUTs are provided beforehand incorrespondence with the type of inks and a medium used in the printer 17b and the like. Then, when color conversion processing is performed, anappropriate color correction LUT is selected. This embodiment is also soconstituted that an appropriate color correction LUT is selected andutilized. In case of this embodiment, one of these color correction LUTsis the color correction LUT generated by the color correction LUTgenerator 20A.

[0111] When the predetermined color correction LUT is selected (Step 72,YES), that color correction LUT is read out of the color correction LUTstoring portion 20 b and into the RAM 12 f (Step 74). Then, the colorcorrection LUT is incorporated into the color correcting portion 20 a(Step 76). Image processing is performed by interpolation referring tothe three-dimensional color correction LUT, and image output processingis performed (Step 78). That is, CMYKlclm image output data is obtained.The printer driver 12 c further processes this CMYKlclm image outputdata, and performs the print operation.

[0112] More specifically, using this CMYKlclm image output data, halftone processing, rasterizing processing, and the like are performed, andprint data to be sent out to the printer 17 b is generated in the end.When the generated print data is sent out to the printer 17 b, theprinter 17 b performs the print operation based on the print data. Thecolor correction LUT according to the present invention is created basedon the result of color measuring with respect to lattice points smoothedas described later. As a result, a color correction LUT which enableshighly accurate color conversion throughout color spaces can be created.Thus, a print result without occurrences of tone jump throughout thecolor spaces can be obtained.

[0113] With the color correction LUT in this embodiment, pieces of imagedata in different color spaces can be brought into correspondence witheach other. Further, image data of an arbitrary color can be computed byinterpolation from a plurality of representative colors defined in thecolor correction LUT. Therefore, color spaces which are brought intocorrespondence with each other by the color correction LUT are notlimited to sRGB or CMYKlclm mentioned above. Various embodiments, suchas correspondence between equipment-specific RGB colors and CMYKlclmcolors, can be adopted.

[0114] (3) Image Processing Control Program:

[0115] When the printer driver 12 c is executed with the above-mentionedhardware configuration, the computer system l2 in this embodimentthereby functions as an image processor. Therefore, modules whichperform image processing in the printer driver 12 c constitute the imageprocessing control program according to the present invention. Thisimage processing control program is usually recorded on a recordingmedium, such as flexible disk and CD-ROM, in a computer 12-readablemanner, and distributed. The program is read by a media reader (e.g.CD-ROM drive 13 c, flexible disk drive 13 a, etc.) and is installed inthe hard disk 13 b. Then, the CPU 12 e reads required programs from thehard disk 13 b and performs required processing.

[0116] (4) Color Correction LUT Generator:

[0117] Next, processing performed by the color correction LUT generator20A will be described in detail. As illustrated in FIG. 1, the colorcorrection LUT generator 20A comprises a cost computing portion 20 d; aportion 20 e for optimization by evaluation function; a readjustingportion 20 f; a portion 20 g for generating LUT before color matching; acolor measuring data acquiring portion 20 h; a color correction LUTgenerating portion 20 i; and the color correction LUT storing portion 20b. FIG. 5 schematically illustrates the flow of processing in the colorcorrection LUT generator 20A. The cost computing portion 20 d computesterms contained in the CMY lattice point evaluation function and the inkquantity lattice point evaluation function.

[0118] The ink quantity lattice point smoothness evaluation function isa function for evaluating the smoothness of the disposition of inkquantity lattice points whose component is the quantity of each colorink. The color ink quantities are values which specify the quantities ofsix color inks provided and consumed in the printer l7 b. In thisembodiment, the quantities consumed are expressed in 256 (0 to 255)shades of gray. Therefore, a six-dimensional space whose components arethe quantities of these six color inks can be considered. In thisembodiment, this six-dimensional space is referred to as “ink quantityspace.” In the ink quantity space as well, if an ink quantity isdefined, the position in the space is identified, and that point can betaken as a lattice point.

[0119] The CMY lattice point evaluation function is a function forevaluating the smoothness of the disposition of CMY lattice pointsdefined by the color components of CMY. Each component value of the CMYlattice points can be calculated by multiplying a column vector whoseelements are the six components of the above ink quantities by apredetermined matrix with 3 rows and 6 columns. Further, by subtractingeach component value of CMY lattice points from the value of a constant,they can be virtually brought into one-to-one correspondence with thecolor components of RGB. These CMY components will be referred to as“virtual CMY,” and the color space defined by the CMY components will bereferred to as “virtual CMY space.” In consideration of the virtual CMYspace, when the respective values of CMY components are defined, theirpositions in the virtual CMY space can be identified, and these pointscan be taken as lattice points.

[0120] As mentioned above, the virtual CMY can be brought intoone-to-one correspondence with the respective color components of RGBonly by increasing or decreasing the constant. If the lattice pointdisposition is less screwed in the virtual CMY space, the skewness inthe lattice point disposition is reduced in the RGB color space as well.Therefore, by optimizing the lattice point disposition in the virtualCMY space, it is guaranteed that the skewness in the lattice pointdisposition in the RGB color space is reduced. Therefore, these latticepoints are suitable for creating color correction LUTs which definecorrespondence between sRGB image data and CMYKlclm image data as inthis embodiment. The ink quantity space is six-dimensional and thevirtual CMY space is three-dimensional. Therefore, when compared withthe ink quantity space, the virtual CMY space is the lower-dimensionalcolor space.

[0121] As mentioned above, the ink quantity lattice point smoothnessevaluation function and the CMY lattice point smoothness evaluationfunction are functions for evaluating the smoothness of the dispositionof lattice points in the respective color spaces. Also, they arefunctions which optimize the positions of lattice points by minimizationof the respective functions. Therefore, each term in these functions isa function whose value is reduced as the disposition of lattice pointsis smoothed. This is referred to as “cost.” The cost computing portion20 d is capable of separately computing the costs 20 d 1 in the CMYlattice point evaluation function and the costs 20 d 2 in the inkquantity lattice point evaluation function. When the cost computingportion 20 d computes the costs in the individual functions, the CMYlattice point evaluation function and the ink quantity lattice pointevaluation function are determined by the sum thereof.

[0122] The portion 20 e for optimization by evaluation function utilizesthe determined CMY lattice point evaluation function and ink quantitylattice point evaluation function to optimize the lattice pointpositions in the respective color spaces. More specifically, the portion20 e computes the minimal solution of each evaluation function, anddefines the lattice point position wherein the minimal solution is givenas the optimal lattice point position. The portion 20 e for optimizationby evaluation function separately utilizes the individual evaluationfunctions to optimize the lattice point positions in the respectivecolor spaces. Various algorithms can be adopted as the algorithm forcomputing the minimal solution. Different algorithms may be adopted forthe CMY lattice point evaluation function and for the ink quantitylattice point evaluation function. Or, the same algorithm may be adoptedfor both the functions. If it is required that either lattice pointposition should be optimized more accurately, an algorithm which allowseither to be optimized more accurately can be adopted.

[0123] According to the present invention, the calculation of costs andthe optimization of evaluation functions are individually performed withrespect to each color space, as mentioned above. In this embodiment,this is implemented at Step 100 to Step 130 in FIG. 5. Morespecifically, at Step 100, the cost computing portion 20 d computescosts with respect to the virtual CMY space. At Step 110, the portion 20e for optimization by evaluation function performs optimization by theCMY lattice point evaluation function. Further, at Step 120, the costcomputing portion 20 d computes costs with respect to the ink quantityspace. At Step 130, the portion 20 e for optimization by evaluationfunction performs optimization by the ink quantity lattice pointevaluation function. Needless to add, Steps 120 and 130 may be carriedout before Steps 100 and 110. This is because the CMY lattice pointevaluation function and the ink quantity lattice point evaluationfunction only have to be individually optimized.

[0124] According to the present invention, each component value of CMYlattice points is computed by multiplying an ink quantity by a matrix,as mentioned above. However, lattice point disposition is separatelyoptimized with respect to CMY lattice points and to ink quantity latticepoints, as mentioned above. Therefore, after the optimization, therelation defined by the above matrix is not maintained between CMYlattice points and ink quantity lattice points. The present invention isintended to determine optimized lattice points for correspondencedefinition data creation, which are used when a color correction LUT isgenerated, both in the virtual CMY space and in the ink quantity space.

[0125] Consequently, in the color correction LUT generator 20A, thereadjusting portion 20 f prevents the lattice point dispositions,separately optimized in the virtual CMY space and in the ink quantityspace, from being moved as much as possible. Further, the readjustingportion 20 f also readjusts the lattice point dispositions so that thecorrespondence defined by the above matrix will hold (Step 140). In thisembodiment, the CMY lattice points in the virtual CMY space are storedat the optimized value, and the ink quantity lattice points are moved.The ink quantity space is a six-dimensional space. Therefore, minimalsolutions are likely to be larger in number in the ink quantity latticepoint evaluation function than in the CMY lattice point evaluationfunction which is an evaluation function for three-dimensional lattices.Thus, it is more difficult to discriminate a true solution.

[0126] Therefore, CMY lattice points are easier to converge in the trueoptimal value. In this embodiment, CMY lattice points, which areexpected to have converged in the true optimal value, are fixed, and inkquantity lattice points are moved. Needless to add, it is notindispensable to fix CMY lattice points even in cases where with CMYlattice points fixed, it is impossible to determine the ink quantityspace which minimizes the ink quantity lattice point evaluationfunction. When the print operation is performed with the printer 17 b asin this embodiment, in general, the quantity of ink injectable per unitarea in a printing medium is limited. Further, limitation is imposed toprevent inks of specific color components from being used for specificcolors.

[0127] The color correction LUT generated in this embodiment is alook-up table with these conditions also taken into account. In thisembodiment, these conditions are imposed as binding conditions inreadjustment. As a result, the following ink quantity lattice points canbe computed: lattice points which identify ink quantities whereinlimitations are met with respect to the quantity of ink injectable perunit area in a printing medium and to the prevention of use of inks ofspecific color components for specific colors, and whose disposition inthe ink quantity space is optimized. Limitation on the quantity of inkinjectable per unit area in a printing medium and limitation to preventinks of specific color components for specific colors are limitationsimposed on ink quantity. Therefore, these conditions can be convenientlyimposed by adopting such an embodiment that the ink quantity isreadjusted after individual optimization, like this embodiment.

[0128] By the above-mentioned processing, specific lattice points aredetermined with the optimal disposition both in the virtual CMY spaceand in the ink quantity space and other various conditions taken intoaccount. Consequently, a plurality of lattice points are subjected tothe above-mentioned optimization so that the entire color spaces will becovered. Thus, LUT which brings CMY lattice points and ink quantitylattice points into correspondence with each other throughout the colorspaces can be generated. In this embodiment, the lattice pointdisposition is optimized by minimization of the evaluation functions.Each lattice point is optimized by carrying out a plurality of times ofcorrection (a plurality of times of minimization).

[0129] Accordingly, at Step 150, the portion 20 g for generating LUTbefore color matching judges whether all the rounds of correction havebeen completed with respect to all the lattice points. The portion 20 grepeats the processing of Step 100 and the following steps with respectto each lattice point until the completion of correction is judged. Inthe above description, lattice points which cover the entire colorspaces are referred to. However, needless to add, these arerepresentative points and an finite number of lattice points. Withrespect to the number of lattice points, tone jump only has to beprevented from occurring when a color correction LUT is generated. Forexample, the above processing only has to be performed with respect to1,000 lattice points. After all the rounds of correction have beencarried out with respect to all the lattice points, LUT before colormatching (before color measuring to be described later) is generated.

[0130] At Step 160, the color measuring data acquiring portion 20 h andthe color correction LUT generating portion 20 i generate a colorcorrection LUT to be used in actual color conversion. That is, in thecolor correction LUT, it is required that colors specified by sRGB imagedata and color printed with CMYKlclm image data should be matched witheach other. The colors specified by sRGB image data are univocallydefined. Meanwhile, the output colors in ink quantities defined byCMYKlclm image data are dependent on equipment. Therefore, colormeasuring is performed to determine actual colors, and further, thecolor correction LUT is defined.

[0131] More specifically, a print patch wherein color components of theink quantity lattice points are taken as the components of CMYKlclmimage data is printed. Then, the color measuring data acquiring portion20 h acquires color measuring data obtained from color measuring by acolor measuring instrument or the like. As a result, data wherein colorsindicated by the ink quantity lattice points are rendered bynon-equipment-dependent colors is obtained. With respect to sRGB imagedata, colors therein can be brought into correspondence withnon-equipment dependent colors by publicly known formulas. Therefore, ifa table which brings lattice points obtained by color measuring and sRGBvalues obtained from the color measuring values into correspondence witheach other is generated, that table can be used as a color correctionLUT. Color correction LUTs are generated by the above color correctionLUT generating portion 20 i.

[0132] In general, the number of representative colors defined by acolor correction LUT is made larger than that of the lattice points forcorrespondence definition data creation. It is troublesome to subjecttoo many patches to color measuring. Therefore, correspondence may becomputed by subjecting some colors to color measuring and the othercolors to interpolation determined from lattice points which has beensubjected to the color measuring. For example, if with respect to 1,000lattice points, patches are subjected to color measuring, as mentionedabove, the number of lattice points may be reduced to 173 by usinginterpolation. Once a color correction LUT is generated, as mentionedabove, the color correction LUT storing portion 20 b stores the colorcorrection LUT on a predetermined storage medium (Step 170).

[0133] (5) Optimization by CMY Lattice Point Evaluation Function:

[0134] Next, cost computation and optimization carried out when the CMYlattice point evaluation function is optimized will be described indetail. In this specification, description will be given below withlattice points in each color space taken as vectors from the originpoint to lattice points in the color space. That is, each lattice pointwill be taken as a column vector whose element is the color componentvalue of that lattice point. In the first stage of optimization, inkquantity vector Ipn is determined as the initial value of ink quantitylattice point.

[0135] Since the disposition of ink quantity lattice points isoptimized, there is no special limitation on methods for selecting theinitial value of ink quantity lattice point. For example, lattice pointsgenerated by uniformly varying the color components of ink quantitylattice points maybe adopted. Here, p is the number for a lattice point,and the following description will be given on the assumption that thenumber of all the lattice points is P, that is, 1≦p≦P. n represents thenumber of times of correction, and, letting the total number of times ofcorrection be N, 0≦n≦N. (n=0 represents the initial state beforecorrection.) Therefore, in a series of optimization, N times ofcorrection are attempted with respect to all the P lattice points(1≦p≦P) to optimize the positions of the lattice points.

[0136]FIG. 6 is a flowchart which illustrates in detail the processingpreformed at Steps 100 and 110 in FIG. 5, and this processing isperformed after the ink quantity vector Ipn is determined. At Step 102,CMY vector Spn is computed. The CMY vector is a vector which specifieslattice points in the virtual CMY space.

[0137] As mentioned above, the component values of CMY lattice pointscan be calculated by multiplying a column vector whose elements are thesix components of ink quantity by a predetermined matrix K with 3 rowsand 6 columns. At Step 102, Spn is computed by Formula (1) below.

[0138] [Expression 1]

S _(p) ^(n) =K·I _(p) ^(n)  (1)

[0139] In the formula, the vector quantity and the matrix are indicatedin bold type. (This is the same with the following description.)

[0140] Next, at Step 104, CMY lattice point evaluation function E spn iscomputed. CMY lattice point evaluation function Espn is given by Formula(2) below.

Espn=Estpn+Esopn+Esapn  (2)

[0141] In this embodiment, the CMY lattice point evaluation function isexpressed as the sum of cost terms whose value is reduced as thedisposition of lattice points is smoothed.

[0142] Estpn is a cost for evaluating the smoothness of the dispositionof CMY lattice points, and is a function whose value is increased as thesmoothness is degraded.

[0143] Esopn is a cost for evaluating whether a CMY lattice point isclose to a specific position, and is a function whose value is increasedas the CMY lattice point gets away from a specific position.

[0144] Esapn is a cost for evaluating whether the color indicated by aCMY lattice point is close to a specific color, and is a function whosevalue is increased as the color indicated by the CMY lattice pointdeparts from a specific color. These costs are all scalar quantities, asdescribed later.

[0145] Each term will be described in detail below. However, it is notalways required to use all the terms, but terms to be used may beselected as required. That is, according to the present invention, theterms in the CMY lattice point evaluation function and the ink quantitylattice point evaluation function to be described later, which terms arecost term Ec with respect to some vector X can be written as GeneralFormula (3). Every condition that corresponds to this General Formula(3) can be sorted out and incorporated as a cost term.

[0146] [Expression 2] $\begin{matrix}{\lbrack {{Expression}\quad 2} \rbrack {{E\quad c} = \{ \begin{matrix}{{W_{1}^{t} \cdot ( {{M \cdot X} - Y_{T}} )}\quad} \\{{W_{2} \cdot ( {{M \cdot X} - Y_{T}} )}}^{2}\end{matrix} }} & (3)\end{matrix}$

[0147] where,

[0148] Ec is a cost (scalar value);

[0149] X is a column vector whose number of elements is X;

[0150] M is a Y×X matrix, which is a transformation matrix fortransforming vector X into vector Y=MX whose number of elements is Y andwhich is handled in a cost;

[0151] YT is a column vector whose number of elements is Y;

[0152] W 1 is a column vector whose number of elements is Y and is avector which represents weight for each element of vector Y−Y T withrespect to a cost;

[0153] W 2 is a diagonal matrix of Y×Y and is a matrix which representsweight for each element of vector Y−YT with respect to a cost; and tindicates transposition.

[0154] In the following description, the first equation in Formula (3)will be referred to as “primary expression form,” and the secondequation will be referred to “quadratic expression form.”

[0155] (5-1) Cost Estpn:

[0156] Attention will be focused on a CMY lattice point of number p, anda lattice point adjacent to the lattice point p will be let to be pj(hereafter, referred to as “reference lattice point”). A lattice pointwhich adjoins to the lattice point p and is not the lattice point pjwill be let to be pv (hereafter, referred to as “transition latticepoint”). A lattice point which is a lattice point pvj adjacent to thetransition lattice point pv and whose relative positional relation withthe transition lattice point pv is similar to the relative positionalrelation between the lattice point p and the reference lattice point p jwill be referred to as “transition reference lattice point pvj.” Thatis, the direction in which the reference lattice point pj is viewed fromthe lattice point p is similar to the direction in which the transitionreference lattice point pvj is viewed from the transition lattice pointpv. The reference lattice point pj and the transition lattice point pvmay be identical with each other.

[0157] As mentioned above, the vector which represents the lattice pointp is Spn. In correspondence with this, column vectors whose elements arethe color component values of the lattice points pj, pv, and pvj will belet to be vectors Spjn, Spvn, and Spvjn, respectively. FIG. 7illustrates the positional relation between these lattice points. Inthis embodiment, the relative positional relation between the latticepoint p of interest and the reference lattice point pj is compared withthe relative positional relation between the transition lattice point pvand the transition reference lattice point pvj, and thereby thesmoothness of the disposition of lattice points is evaluated.

[0158] Consequently, it is assumed that the relative positional relationbetween the lattice point p of interest and the reference lattice pointpj is maintained and further the lattice point p of interest is causedto transition to the transition lattice point pv. The smoothness of thedisposition of lattice points is evaluated by computation utilizingdifferential vectors. First, the differential vector (Spjn−Spn) betweenvector Spjn and vector Spn and the differential vector (Spvjn−S pvn)between vector Spvjn and vector Spvn are considered. Then, the valueobtained by dividing the variation between differential vector(Spjn−Spn) and differential vector (Spvjn−Spvn) by a transition distanceDsv is defined as torsion quantity vector. That is, the variation ofdifferential vectors per unit transition distance is defined as torsionquantity vector.

[0159] This torsion quantity vector gets smaller as the relativepositional relation between the transition lattice point pv and thetransition reference lattice point pvj resembles the relative positionalrelation between the lattice point p of interest and the referencelattice point pj. For example, in a three-dimensionally orthogonal cubiclattice, the torsion quantity is “0.” In this embodiment, lattice pointpj and lattice point pv are considered with respect to a lattice point pand all the lattice points adjacent thereto. Then, in every combinationof them, the value obtained by adding the square of the magnitude of thetorsion quantity vector is defined as a cost for evaluating thesmoothness of the disposition of individual lattice points.

[0160] That is, it is defined by Formula (4) below. $\begin{matrix}{\lbrack {{Expression}\quad 3} \rbrack {{E\quad s\quad t_{p}^{\quad n}} = {\sum\limits_{v = 1}^{V}\quad {\sum\limits_{j = 1}^{J}\quad {\frac{S_{p}^{n} + S_{p\quad {vj}}^{n} - S_{p\quad v}^{n} + S_{p\quad j}^{n}}{D\quad s_{v}}}^{2}}}}} & (4)\end{matrix}$

[0161] where, j and v are the lattice point number for the referencelattice point and the transition lattice point, respectively; and J andV represent the number of reference lattice points and the number oftransition lattice points, respectively. Various lattice points may beselected as reference lattice point or transition lattice point. Latticepoints including a lattice point most adjacent to the lattice point p orincluding the most adjacent lattice point and the second-adjacentlattice point may be selected. As an example, a case where correction iscarried out with a three-dimensional cubic lattice taken as the initiallattice point positions will be considered. In this case, six adjacentlattice points, positioned above, under, on the left and right of, infront of, and behind the lattice point p, may be selected. Or, 26lattice points including those positioned in the diagonal directions maybe selected.

[0162] Here, Formula (4) will be compared with the second equation ofFormula (3). It is unnecessary to transform the CMY vector S into avector in another space. Therefore, M turns out to be a unit matrix andmay be omitted. Further, any element is not weighted. Therefore, vectorW 2 similarly turns out to be a unit vector and may be omitted. (1/Dsv)2is a constant with respect to some transition lattice point pv.Therefore, the second equation of Formula (3) and Formula (4) are in thesame form.

[0163] (5-2) Cost Esopn:

[0164] Esopn is a cost for evaluating whether a CMY lattice point isclose to a specific position. In this embodiment, a CMY vector beforecorrection is adopted as the specific position. That is, when the CMYvector Spn+1 is calculated in the (n+1) th round of correction, the CMYvector Spn calculated in the nth round of correction is utilized as thespecific position. Cost Esopn is defined by Formula (5).

[0165] [Expression 4]

Eso _(p) ^(n) =|Wso·(S _(p) ^(n) −S _(p) ^(n))|²  (5)

[0166] where, Wso is a diagonal matrix wherein the weight for eachelement of the CMY vector S is defined. When correction is carried out,in the CMY vector Spn of the second term in the parentheses, thecomponent value of the lattice point p obtained from the nth round ofcorrection is substituted to obtain a constant value. Then, the CMYvector Spn of the first term in the parentheses is considered as anindependent variable.

[0167] In such an optimal value search problem that correction isrepeated more than once to gradually reduce a cost, the CMY vector Spnis expected to approach an ideal value with increase in the number oftimes of correction. In reality, however, it dose not always approach anideal value each time one round of correction is carried out. Forexample, the value of the CMY vector Spn diverges or oscillatessometimes. This divergence or oscillation frequently occurs if the CMYvector Spn is drastically moved when the (n+1)th correction is carriedout subsequently to the nth correction. To cope with this, Cost Esopn istaken into account in this embodiment. Thus, the divergence andoscillation can be effectively prevented, and the CMY vector Spn can beswiftly converged.

[0168] That is, the cost shown in Formula (5) is increased as the CMYvector Spn+1 is largely varied from Spn as the result of the (n+1) thcorrection. Therefore, by incorporating this cost term in the CMYlattice point evaluation function, the CMY vector S is prevented fromlargely fluctuating by one round of correction. The influences offluctuation in CMY vector S on costs can be adjusted by the weight ofeach element of the diagonal matrix Wso.

[0169] According to this cost Es opn, the divergence and oscillation canbe prevented and in addition, binding conditions which reflect variousintentions can be obtained. For example, such a condition as to preventreduction in the color saturation of a color indicated by a CMY latticepoint p can be imposed. To do this, a position wherein the colorequivalent to the color saturation of the color indicated by the latticepoint p is taken as the specific position. Thus, a binding conditionwhich does not unnecessarily lower the color saturation can be imposed.In this case, a CMY vector Stpn having the color saturation at the samelevel as the color saturation of the color indicated by the CMY vectorSpn may be defined, and thereby, the cost shown in Formula (6) below maybe obtained.

[0170] [Expression 5]

Eso _(p) ^(n) =|Wso·(S _(p) ^(n) −St _(p) ^(n))|²  (6)

[0171] Needless to add, the color indicated by a CMY lattice point isnot always strictly defined. This is because the color component thereofis determined by multiplication of the matrix K and the ink quantityvector Ipn. However, the color saturation is prevented from beingunnecessarily lowered due to repeated correction. This is done byanticipating a color determined by at least the CMY vector S and furtherdetermining the color saturation; defining a CMY vector Stpn having thecolor saturation at the same level as the color saturation; andincorporating it in a cost term. It can be confirmed that Formulas (5)and (6) above are also in the same form as the second equation ofFormula (3) above.

[0172] As mentioned above, in addition to a condition for preventingreduction in color saturation, a condition for maintaining appropriatememorized colors can be imposed. With respect to colors, such as gray,flesh color, green, and blue, which are different from correspondingcolors memorized by humans, color correction LUTs are sometimes adjustedso that a color close to a corresponding color memorized by humans willbe outputted. With respect to such colors, lattice point dispositionwherein the memorized color is easy to maintain can be selected, and aCMY vector Stpn which indicates the lattice point disposition can bedefined.

[0173] (5-3) Cost Esapn:

[0174] Esapn is a cost for evaluating whether a color indicated by a CMYlattice point is close to a specific color. In this embodiment, a colorwherein any one of the components of CMY vector S is “0” or a colorwhose components are equivalent, that is, an achromatic color is adoptedas the specific color. Hereafter, colors wherein any two components ofCMY vector S are “0” will be referred to as “primary colors” and thosewherein any one component is “0” will be referred to as “secondarycolors.” Achromatic colors include a case where all the components are“0.”

[0175] In this embodiment, a function whose value is increased when acolor indicated by a CMY lattice point deviates from a primary color, asecondary color, or an achromatic color is used as Cost Esapn. The costis defined by Formula (7) below.

[0176] [Expression 6]

Esa _(p) ^(n) =|Wsa _(p) ·H·S _(p) ^(n)|²  (7)

[0177] where, H is a matrix with 6 rows and 3 columns, defined byFormula (8) below; and Wsap is a diagonal matrix which is a weightingmatrix indicating the weight for each element transformed by H·Spn,defined by Formula (9) below.

[0178] [Expression 7] $\begin{matrix}{\lbrack {{Expression}\quad 7} \rbrack {H = \begin{pmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\1 & {- 1} & 0 \\0 & 1 & {- 1} \\{- 1} & 0 & 1\end{pmatrix}}} & (8)\end{matrix}$

[0179] [Expression 8] $\begin{matrix}{\lbrack {{Expression}\quad 8} \rbrack {{Wsa}_{p} = \begin{pmatrix}{wsa}_{pc} & 0 & 0 & 0 & 0 & 0 \\0 & {wsa}_{pm} & 0 & 0 & 0 & 0 \\0 & 0 & {wsa}_{py} & 0 & 0 & 0 \\0 & 0 & 0 & {wsa}_{pcm} & 0 & 0 \\0 & 0 & 0 & 0 & {wsa}_{pmy} & 0 \\0 & 0 & 0 & 0 & 0 & {wsa}_{pyc}\end{pmatrix}}} & (9)\end{matrix}$

[0180] More specific description will be given. The color components ofCMY vector S will be let to be (scpn, smpn, sypn). Thus, the result oftransformation by the H·Spn is vector (scpn, smpn, sypn, scpn−smpn,smpn−sypn, −scpn+sypn). The components of matrix Wsap are defined sothat finite values will be given to those on which a binding conditionis imposed, of the components of this vector.

[0181] For example, in case of the primary color of cyan, the magentacomponent and the yellow component must be “0.” That is, a cost isdefined so that the value thereof will be increased by the magentacomponent and yellow component having finite values. In this case, theelements, other than the elements wsapm and wsapy, of the weightingmatrix Wsap are set to “0,” and finite values are given tows apm andwsapy. When Formula (7) above is expanded in this situation, Formula(10) below is obtained.

[0182] [Expression 9]

Esa _(p) ^(n)=(wsa _(pm) ·S _(mp) ^(n))²+(wsa _(py) ·S _(yp)^(n))²  (10)

[0183] As is evident from Formula (10), when the magenta component smpnand the yellow component sypn of CMY vector Spn have a value other than“0” Cost Esapn has a finite value. Therefore, the primary color of cyancan be prevented from deviating from the primary color, by reducing CostEsapn as much as possible. In cases where a color deviates from anotherprimary color or secondary color, a cost can be similarly considered.

[0184] Next, a case where, for example, blue is rendered by makingequivalent the cyan component and the magenta component of CMY vectorSpn will be considered. At this time, the elements other than wsapcm ofweighting matrix Wsap are set to “0,” and a finite value is given towsapcm. When Formula (7) above is expanded in this situation, Formula(11) below is obtained.

[0185] [Expression 10]

Esa _(p) ^(n) ={wsa _(pcm)(S _(cp) ^(n) −S _(mp) ^(n))}²  (11)

[0186] As is evident from Formula (11), if the cyan component s cpn andthe magenta component smpn of CMY vector Spn are not equivalent, CostEsapn has a finite value. Therefore, a situation wherein the cyancomponent and the magenta component are equivalent is prevented frombeing deviated from, by reducing Cost Esapn as much as possible. Incases where the cyan component and the yellow component are madeequivalent or the yellow component and the magenta component are madeequivalent, a cost can be similarly considered. As in these examples,the weighting elements of Wsap can take various values depending on theconditions of the lattice point p.

[0187] Needless to add, in this embodiment, Cost Esapn is not acondition imposed on the lattice point of every number p. But it is acondition imposed on a lattice point of a specific lattice point number.When an image is handled with a computer, the gradation value thereof isoften limited to a positive value. According to this embodiment, withrespect to a color any color component of which is “0,” Cost Esapn is afunction whose value is increased as that component deviates from “0.”This can be considered as imposing a condition for preventing any colorcomponent from becoming negative. Formula (7) above corresponds to thesecond equation of Formula (3) above with YT set to “0.” Needless toadd, if a maximum value is defined for the gradation value of each colorcomponent, a function whose cost is increased when the coordinate valueis greater than the maximum value may be adopted.

[0188] (5-4) Computation of Vector Which Gives Minimal Value:

[0189] Once the individual cost terms are computed, as mentioned above,CMY lattice point evaluation function Espn can be obtained by Formula(2) above. Then, the processing of steps up to Step 104 in FIG. 6 iscarried out. Thereafter, at Step 112 to Step 116, the minimal value ofCMY lattice point evaluation function Espn is computed, and optimizationis thereby carried out. There are various techniques for computing theminimal value of CMY lattice point evaluation function Espn. In thisembodiment, the following technique is adopted which makes it possibleto effectively prevent the components of CMY lattice points fromoscillating or diverging.

[0190] The CMY lattice point evaluation function Espn is the sum ofFormulas (4), (5), and (7), and the CMY vector Spn is contained in allof these terms. Therefore, the CMY lattice point evaluation functionEspn is a function of CMY vector Spn. That is, it can be expressed by afunction fs, as in Formula (12) below.

[0191] [Expression 11]

Es _(p) ^(n) =fs(S _(p) ^(n))  (12)

[0192] Here, it is assumed that the CMY lattice point evaluationfunction Espn can take the minimum value if correction quantity vectorep is added to the CMY vector Spn. Thus, the vector obtained bypartially differentiating Formula (13) below with the elements of CMYvector Spn becomes a zero vector. This is expressed by Formula (14).

[0193] [Expression 12]

Es _(p) ^(n) =fs(S _(p) ^(n) +e _(p))  (13)

[0194] [Expression 13] $\begin{matrix}\lbrack {{Expression}\quad 13} \rbrack & (14) \\{{A\quad s_{p}^{\quad n}} = {{\frac{\partial\quad}{\partial s_{q\quad p}^{\quad n}}f\quad {s( {S_{p}^{\quad n} + e_{p}} )}} = 0_{3}}} & \quad \\{\quad ( {{q = c},m,y} )} & \quad\end{matrix}$

[0195] where, sqpn represents the component of CMY vector Spn; and qrepresents the identification of the component. The components of vectorAspn are obtained by partially differentiating Formula (13) with scpn,smpn, and sypn, respectively.

[0196] In this embodiment, Formula (14) above is solved with respect tothe correction quantity vector ep, and the CMY vector from the (n+1) thcorrection is obtained from the CMY vector from the nth correction byFormula (15) below.

[0197] [Expression 14]

S _(p) ^(n+1) =S _(p) ^(n) +λe _(p)  (15)

[0198] where, λ is an arbitrary scalar value and a coefficient relatedto the correction quantity vector ep, in general, 0≦λ≦1. If λ=1, itturns out that Formula (14) above is directly solved.

[0199] In this embodiment, by making adjustment within a range of 0≦λ≦1, the CMY vector is caused to efficiently converge, and further, thecomponents of CMY lattice points are prevented from oscillating ordiverging.

[0200] More specifically, the first equation of Formula (14) isexpressed as in Formulas (16) to (19) below.

[0201] [Expression 15]

A _(p) ^(n) =Ast _(p) ^(n) +Aso _(p) ^(n) +Asa _(p) ^(n)  (16)$\begin{matrix}\lbrack {{Expression}\quad 15} \rbrack & (16) \\{{A\quad s_{p}^{n}} = {{A\quad s\quad {t\quad}_{p}^{n}} + {A\quad s\quad o_{p}^{\quad n}} + {A\quad s\quad a_{p}^{n}}}} & \quad \\{{A\quad {st}_{p}^{\quad n}} = {\frac{\partial\quad}{\partial s_{q\quad p}^{\quad n}}\{ {\sum\limits_{v = 1}^{V}\quad {\sum\limits_{j = 1}^{J}\quad {\frac{( {S_{p}^{n} + e_{p}} ) + S_{p\quad v\quad j}^{n} - S_{p\quad v}^{n} - S_{p\quad j}^{n}}{D\quad s_{v}}}^{2}}} \}}} & (17) \\{\quad {= {{2\quad {J( {\sum\limits_{v = 1}^{V}\frac{1}{D\quad s_{v}^{2}}} )}( {S_{p}^{n} + e_{p}} )} - {2J{\sum\limits_{v = 1}^{V}\frac{S_{p\quad v}^{n}}{D\quad s_{v}^{2}}}} +}}} & \quad \\{\quad {2{\sum\limits_{v = 1}^{V}\{ {\frac{1}{D\quad s_{v}^{2}}{\sum\limits_{j = 1}^{J}( {S_{p\quad v\quad j}^{n} - S_{p\quad j}^{n}} )}} \}}}} & \quad \\{{A\quad s\quad o_{p}^{n}} = {\frac{\partial\quad}{\partial s_{q\quad p}^{\quad n}}\lbrack {{W\quad s\quad {o \cdot \{ {( {S_{p}^{n} + e_{p}} ) - {S\quad t_{p}^{\quad n}}} \}}}}^{2} \rbrack}} & (18) \\{\quad {= {{2W\quad s\quad {o^{t} \cdot W}\quad s\quad {o \cdot ( {S_{p}^{n} + e_{p}} )}} - {2W\quad s\quad {o^{t} \cdot W}\quad s\quad {o \cdot S}\quad t_{p}^{\quad n}}}}} & \quad \\{{A\quad s\quad a_{p}^{n}} = {\frac{\partial\quad}{\partial s_{q\quad p}^{\quad n}}\{ {{W\quad s\quad {a_{p} \cdot H \cdot ( {S_{p}^{n} + e_{p}} )}}}^{2} \}}} & (19) \\{\quad {= {2{( {{Ws}\quad {a_{p} \cdot H}} )^{t} \cdot {Ws}}\quad {a_{p} \cdot H \cdot ( {S_{p}^{n} + e_{p}} )}}}} & \quad\end{matrix}$

[0202] where, Astpn, Asopn, and Asapn, respectively, represent vectorsobtained by partially differentiating Estpn, Esopn, and Esapn with thecomponents of CMY vector Spn; and t represents the transposition of amatrix q in Formulas (17) to (19) is the same as the above-mentioned q,which is a sign for identifying the components of vectors. In Formula(17), Dsv is calculated using the components of CMY vector Spn. However,in this embodiment, it is handled as a constant for the simplificationof processing.

[0203] If Formula (14) is solved utilizing Formulas (16) to (19) withrespect to the correction quantity vector ep, the result is expressed asFormula (20). In Formula (20), Qs is expressed by Formula (21), and Bsis expressed by Formula (22). “−1” in Formula (20) indicates inversematrix, and U in Formula (21) indicates unit matrix.

[0204] [Expression 16]

e _(p) =Qs ⁻¹ ·Bs  (20) $\begin{matrix}\lbrack {{Expression}\quad 16} \rbrack & (20) \\{e_{p} = {Q\quad {s^{- 1} \cdot B}\quad s}} & \quad \\{Q_{s} = {{{J( {\sum\limits_{v = 1}^{V}\quad \frac{1}{D\quad s_{v}^{2}}} )}U_{3}} + {{Wso}^{t} \cdot {Wso}} + {( {{Wsa}_{p} \cdot H} )^{t} \cdot {Wsa}_{p} \cdot H}}} & (21) \\{{B\quad s} = {{J{\sum\limits_{v = 1}^{V}\frac{S_{pv}^{n}}{D\quad s_{v}^{2}}}} - {\sum\limits_{v = 1}^{V}\{ \quad {\frac{1}{D\quad s_{v}^{2}}{\sum\limits_{j = 1}^{J}\quad ( {S_{{pv}\quad j}^{n} - S_{pj}^{n}} )}} \}} +}} & (22) \\{\quad {{{Wso}^{t} \cdot {Wso} \cdot {St}_{p}^{\quad n}} - {{Qs} \cdot S_{p}^{\quad n}}}} & \quad\end{matrix}$

[0205] According to Formula (20), the correction quantity vector e p inFormula (15) above can be calculated. Therefore, if λ is determined, CMYvector Spn+1 from the (n+1)th correction can be calculated. In thisembodiment, at Step 112 in FIG. 6, the correction quantity vector ep iscalculated by Formula (20), and, letting λ=1, the CMY vector Spn+1 iscalculated by Formula (15) with respect to 1≦p≦P. At Step 114, the CMYvector Spn+1 is substituted for the CMY vector Spn in Formulas (4), (5),and (7) to calculate the (n+1) th value of CMY lattice point evaluationfunction Espn+1 (1≦p≦P).

[0206] Here, if Espn+1>Espn, λ is reduced, and the CMY vector Spn+1 iscalculated again (Step 116). More specific description will be given. IfEspn+1>Espn, it cannot be said that the disposition of CMY latticepoints has been smoothed by the (n+1) th correction. Therefore, λ isreduced, and thereby, the quantity of the (n+1)th correction is reduced.Various techniques are available for calculating λ. In this embodiment,Formula (23) below is adopted.

[0207] [Expression 17] $\begin{matrix}\begin{matrix}{\lbrack {{Expression}\quad 17} \rbrack \quad} \\{\lambda = \{ \begin{matrix}( \frac{E\quad s_{p}^{n}}{E\quad s_{p}^{n + 1}} )^{2} & ( {{E\quad s_{p}^{n + 1}} > {E\quad s_{p}^{n}}} ) \\1 & ( {{E\quad s_{p}^{n + 1}} \leqq {E\quad s_{p}^{n}}} )\end{matrix} }\end{matrix} & (23)\end{matrix}$

[0208] λ is determined by Formula (23) above, and the CMY vector Spn+1is eventually determined by Formula (15) above with respect to all thelattice point numbers p (1≦p≦P). Various techniques can be adopted asthe technique for calculating λ, as mentioned above. The comparison ofCosts Estpn and Estpn+1 is also acceptable.

[0209] (6) Optimization by Ink Quantity Lattice Point EvaluationFunction:

[0210] Next, cost computation and optimization carried out when the inkquantity lattice point evaluation function is optimized will bedescribed in detail. In the first stage of optimization, ink quantityvector Ipn has been determined as the initial value of ink quantitylattice point, as mentioned above. Cost computation and the optimizationof the evaluation function are carried out utilizing this value. Hereagain, p is the number for a lattice point, and the followingdescription will be given on the assumption that the number of all thelattice points is P, that is, 1≦p≦P. n represents the number of times ofcorrection, and, letting the total number of times of correction be N,0≦n≦N. (n=0 represents the initial state before correction.) Therefore,in a series of optimization, N times of correction are attempted withrespect to all the P lattice points (1≦p≦P) to optimize the positions oflattice points.

[0211] The optimization by the ink quantity lattice point evaluationfunction has been carried out at Step 120 and Step 130 in FIG. 5, asmentioned above. At Step 120, the ink quantity lattice point evaluationfunction Eipn is computed first. The ink quantity lattice pointevaluation function Eipn is given by Formula (24) below.

Eipn=Eitpn+Eiopn  (24)

[0212] In this embodiment, the ink quantity lattice point evaluationfunction is expressed by the sum of cost terms whose value is reduced asthe disposition of lattice points is smoothed. Eitpn is a cost forevaluating the smoothness of the disposition of ink quantity latticepoints, and is a function whose value is increased as the smoothness isdegraded.

[0213] Eiopn is a cost for evaluating whether an ink quantity latticepoint is close to a specific position, and is a function whose value isincreased as the ink quantity lattice point gets away from a specificposition. Each term will be described in detail below. However, it isnot always required to use all the terms, but terms to be used may beselected as required. With respect to the ink quantity lattice pointevaluation function as well, a cost for evaluating whether a colorindicated by an ink quantity lattice point is close to a specific colormay be considered as with the above-mentioned CMY lattice points.

[0214] (6-1) Cost Eitpn:

[0215] Cost Eitpn in the ink quantity lattice point evaluation functioncan be considered similarly with Cost Estpn in the CMY lattice pointevaluation function. Then, the smoothness of the disposition of latticepoints in the ink quantity space can be thereby evaluated. Morespecifically, attention will be focused on an ink quantity lattice pointof number p, and a lattice point adjacent to the lattice point p will belet to be reference lattice point pj. Further, a lattice point whichadjoins to the lattice point p and is not the lattice point pj will belet to be transition lattice point pv. A lattice point which is alattice point pvj adjacent to the transition lattice point pv and whoserelative positional relation with the transition lattice point pv issimilar to the relative positional relation between the lattice point pand the reference lattice point pj will be referred to as “transitionreference lattice point pvj.”

[0216] That is, though the ink quantity space is six-dimensional, thesmoothness of lattice point disposition can be evaluated by definingCost Eitpn similarly with the above-mentioned Cost Estpn. This is doneby defining a lattice point p of interest, a reference lattice point pj,a transition lattice point pv, and a transition reference lattice pointpvj just like the definition with respect to the virtual CMY space. Hereagain, column vectors whose elements are the color component values oflattice points pj, pv, and pvj will be let to be vectors Ipjn, Ipvn, andIpvjn, respectively. FIG. 8 schematically illustrates the positionalrelation between the above-mentioned lattice points.

[0217] Here again, it is assumed that the relative positional relationbetween the lattice point p of interest and the reference lattice pointpj is maintained and further the lattice point p of interest is causedto transition to the transition lattice point pv. The smoothness of thedisposition of lattice points is evaluated by computation utilizingdifferential vectors. Then, the value obtained by dividing the variationbetween differential vector (Ipjn−Ipn) and differential vector(Ipvjn−Ipvn) by a transition distance Div is defined as torsion quantityvector. In other words, the variation in differential vector per unittransition distance is defined as torsion quantity vector.

[0218] The torsion quantity vector is reduced as the relative positionalrelation between the transition lattice point pv and the transitionreference lattice point pvj resembles the relative positional relationbetween the lattice point p of interest and the reference lattice pointpj. In this embodiment, lattice point pj and lattice point pv areconsidered with respect to a lattice point p and all the lattice pointsadjacent thereto. Then, in every combination of them, the value obtainedby adding the square of the magnitude of the torsion quantity vector isdefined as a cost for evaluating the smoothness of the disposition ofindividual lattice points.

[0219] That is, it is defined by Formula (25) below.

[0220] [Expression 18] $\begin{matrix}\begin{matrix}{\lbrack {{Expression}\quad 18} \rbrack \quad} \\{{Eit}_{p}^{\quad n} = {\sum\limits_{v = 1}^{V}{\sum\limits_{j = 1}^{J}\quad {\frac{I_{p}^{n} + I_{pvj}^{n} - I_{pv}^{n} - I_{pj}^{n}}{D\quad i_{v}}}^{2}}}}\end{matrix} & (25)\end{matrix}$

[0221] where, j and v are the lattice point number for the referencelattice point and the transition lattice point, respectively; and J andV represent the number of reference lattice points and the number oftransition lattice points, respectively. Various lattice points maybeselected as reference lattice point or transition lattice point. Latticepoints including a lattice point most adjacent to the lattice point p orincluding the most adjacent lattice point and the second-adjacentlattice point may be selected.

[0222] Here, Formula (25) will be compared with the second equation ofFormula (3). It is unnecessary to transform the ink quantity vector Iinto a vector in another space. Therefore, M turns out to be a unitmatrix and may be omitted. Further, any element is not weighted.Therefore, vector W 2 similarly turns out to be a unit vector and may beomitted. (1/Div)2 is a constant with respect to some transition latticepoint pv. Therefore, the second equation of Formula (3) and Formula (25)are in the same form.

[0223] (6-2) Cost Eiopn:

[0224] Eiopn is a cost for evaluating whether an ink quantity latticepoint is close to a specific position. In this embodiment, an inkquantity vector before correction is adopted as the specific position.That is, when the ink quantity vector Ipn+1 is calculated in the (n+1)th round of correction, the ink quantity vector Ipn calculated in thenth round of correction is utilized as the specific position. Cost Eiopnis defined by Formula (26).

[0225] [Expression 19]

Eio _(p) ^(n) =|Wio·(I _(p) ^(n) −I _(p) ^(n))|²  (26)

[0226] where, Wio is a diagonal matrix wherein the weight for eachelement of the ink quantity vector I is defined. When correction iscarried out, in the ink quantity vector Ipn of the second term in theparentheses, the component value of the lattice point p obtained fromthe nth round of correction is substituted to obtain a constant value.Then, the ink quantity vector Ipn of the first term in the parenthesesis considered as an independent variable.

[0227] Here again, Cost Eiopn is taken into account. Thus, thedivergence and oscillation can be effectively prevented, and the inkquantity vector Ipn can be swiftly converged. The influences offluctuation in ink quantity vector I on costs can be adjusted by theweight of each element of the diagonal matrix Wio. According to thiscost Eiopn as well, the divergence and oscillation can be prevented andin addition, binding conditions which reflect various intensions can beobtained. For example, such a condition as to prevent reduction in thecolor saturation of a color indicated by an ink quantity lattice point pcan be imposed. In this case, an ink quantity vector Itpn having thecolor saturation at the same level as the color saturation of the colorindicted by the ink quantity vector Ipn may defined, and thereby, thecost shown in Formula (27) below may be obtained.

[0228] [Expression 20]

Eio _(p) ^(n) =|Wio·(I _(p) ^(n) −It _(p) ^(n))|²  (27)

[0229] It can be confirmed that Formulas (26) and (27) above are also inthe same form as the second equation of Formula (3) above.

[0230] In addition to a condition for preventing reduction in colorsaturation, a condition for maintaining appropriate memorized colors canbe imposed. Lattice point disposition wherein the memorized color iseasy to maintain can be selected, and an ink quantity vector Itpn whichindicates the lattice point disposition can be defined. The appearanceof a color can be largely changed depending on the light source. Toprevent this, various measures are taken. Such measures include usinginks which have special spectral characteristics for colors which aresusceptible to light sources, and reducing the quantities of specificinks consumed to a certain level or below. In this case, such an inkquantity vector Itpn as to meet these conditions may be defined.

[0231] (6-3) Computation of Vector Which Gives Minimal Value:

[0232] Once the individual cost terms are computed, as mentioned above,ink quantity lattice point evaluation function Eipn can be obtained byFormula (24) above. Then, at Step 130 in FIG. 5, the minimal value ofink quantity lattice point evaluation function Eipn is computed, andoptimization is thereby carried out. There are various techniques forcomputing the minimal value of ink quantity lattice point evaluationfunction Eipn. In this embodiment, a technique which is different fromthat for the optimization of the CMY lattice point evaluation functionis adopted. More specifically, in the optimization of ink quantitylattice point evaluation function, an algorithm is used. This algorithmis inferior in the accuracy of minimal value computation to that for theoptimization of the CMY lattice point evaluation function but enableshigh-speed processing. This is because the disposition of ink quantitylattice points is readjusted as described later. Needless to add, thesame algorithm as for the optimization of the CMY lattice pointevaluation function may be adopted.

[0233] The ink quantity lattice point evaluation function Eipn is thesum of Formulas (25) and (26), and the ink quantity vector Ipn iscontained in all of these terms. Therefore, the ink quantity latticepoint evaluation function Eipn is a function of ink quantity vector Ipn.That is, it can be expressed by a function fi, as in Formula (28) below.

[0234] [Expression 21]

Ei _(p) ^(n) =fi(I _(p) ^(n))  (28)

[0235] Here, when the vector (Formula (29)) obtained by partiallydifferentiating Formula (28) with the components of ink quantity vectorIpn becomes a “0” vector, Eipn is minimized.

[0236] [Expression 22] $\begin{matrix}\begin{matrix}{\lbrack {{Expression}\quad 22} \rbrack \quad} \\{{A\quad i_{p}^{n}} = {{\frac{\partial\quad}{\partial i_{m\quad p}^{n}}f\quad {i( I_{p}^{n} )}} = 0_{M}}}\end{matrix} & (29)\end{matrix}$

[0237] where, impn represents the component of ink quantity vector Ipn;and m represents the identification of the component. That is, in thisembodiment, m=1, 2, . . . 6.

[0238] In this embodiment, Formula (29) above is solved, and the inkquantity vector Ipn is thereby calculated. More specifically, the firstequation of Formula (29) is expressed as in Formulas (30) to (32) below.

[0239] [Expression 23]

Ai _(p) ^(n) =Ait _(p) ^(n) +Aio _(p) ^(n)  (30) $\begin{matrix}\begin{matrix}{{Ait}_{p}^{n} = {\frac{\partial}{\partial i_{mp}^{n}}\{  {\sum\limits_{v = 1}^{V}\quad \sum\limits_{j = 1}^{J}}\quad \middle| \frac{I_{p}^{n} + I_{pvj}^{n} - I_{pv}^{n} - I_{pj}^{n}}{{Di}_{v}} |^{2} \}}} \\{= {{2{J( {\sum\limits_{v = 1}^{V}\quad \frac{1}{{Di}_{v}^{2}}} )}I_{p}^{n}} - {2J{\sum\limits_{v = 1}^{V}\quad \frac{I_{pv}^{n}}{{Di}_{v}^{2}}}} +}} \\{{2{\sum\limits_{v = 1}^{V}\quad \{ {\frac{1}{{Di}_{v}^{2}}{\sum\limits_{j = 1}^{J}\quad ( {I_{pvj}^{n} - I_{pj}^{n}} )}} \}}}}\end{matrix} & (31) \\\begin{matrix}{{Aio}_{p}^{n} = {\frac{\partial}{\partial i_{mp}^{n}}\lbrack | {{Wio} \cdot ( {I_{p}^{n} - {It}_{p}^{n}} )} |^{2} \rbrack}} \\{= {{2{{Wio}^{t} \cdot {Wio} \cdot I_{p}^{n}}} - {2{{Wio}^{t} \cdot {Wio} \cdot {It}_{p}^{n}}}}}\end{matrix} & (32)\end{matrix}$

[0240] where, Aitpn and Aiopn, respectively, represent vectors obtainedby partially differentiating Eitpn and Eiopn with the components of inkquantity vector Ipn. m in Formulas (30) to (32) is the same as theabove-mentioned m, which is a sign for identifying the components ofvectors. In Formula (31), Div is calculated using the components of inkquantity vector Ipn. However, in this embodiment, it is handled as aconstant for the simplification of processing.

[0241] If Formula (29) is solved by Formulas (30) to (32) with respectto the ink quantity vector Ipn and the solution is ink quantity vectorIpn+1 obtained by updating the ink quantity vector Ipn, that isexpressed as Formula (33) below. In Formula (33), Qi is expressed byFormula (34), and Bi is expressed by Formula (35). “−1” in Formula (33)indicates inverse matrix, and U in Formula (34) indicates unit matrix.

[0242] [Expression 24]

I _(p) ^(n+1) =Qi ⁻¹ ·Bi  (33) $\begin{matrix}{{Qi} = {{{J( {\sum\limits_{v = 1}^{V}\quad \frac{1}{{Di}_{v}^{2}}} )}U_{M}} + {{Wio}^{t} \cdot {Wio}}}} & (34) \\\begin{matrix}{{Bi} = {{J{\sum\limits_{v = 1}^{V}\quad \frac{I_{pv}^{n}}{{Di}_{v}^{2}}}} - {\sum\limits_{v = 1}^{V}\quad \{ {\frac{1}{{Di}_{v}^{2}}{\sum\limits_{j = 1}^{J}\quad ( {I_{pvj}^{n} - I_{pj}^{n}} )}} \}} +}} \\{{{Wio}^{t} \cdot {Wio} \cdot {It}_{p}^{n}}}\end{matrix} & (35)\end{matrix}$

[0243] The ink quantity vector Ipn+1 can be calculated as mentionedabove. Therefore, when the ink quantity vector Ipn+1 is eventuallydetermined by Formula (33) above with respect to all the lattice pointnumbers p (1≦p≦P), one round of correction is completed.

[0244] (7) Readjustment Processing:

[0245] At Steps 100 to 130, when the CMY vector Spn+1 and the inkquantity vector Ipn+1 are calculated, the CMY lattice point evaluationfunction Espn and the ink quantity lattice point evaluation functionEipn are separately minimized. Therefore, there is no correlationbetween both the vectors. If the vectors are directly brought intocorrespondence with each other, LUT before color matching is notobtained. Consequently, in this embodiment, the readjustment processingshown in the box of Step 140 is carried out to bring them intocorrespondence with each other.

[0246] Each component of the CMY vector Spn+1 can be calculated bymultiplying each component of the ink quantity vector Ipn+1 by theabove-mentioned matrix K. Therefore, if Formula (1) above is taken as abinding condition and further the ink quantity vector Ipn+1 is moved,predetermined correlation is obtained between both the vectors. Sincewith respect to the ink quantity vector Ipn+1, lattice point positionshave been optimized by the above-mentioned minimization, the shorter themoving distance is the better. Consequently, here again, such anevaluation function as mentioned above is considered. That is, anevaluation function for first readjustment whose costs are increasedwith increase in the movement of the ink quantity vector Ipn+1 isconsidered. Then, an ink quantity vector obtained by minimizing theevaluation function for first readjustment is taken as a vector afterreadjustment.

[0247] However, a solution which minimizes the evaluation function forfirst readjustment cannot always be found. To cope with this, in thisembodiment, the CMY vector Spn+1 is moved if no solution is found. Sincethe CMY lattice points have been optimized, here again, it is avoided asmuch as possible to move CMY lattice points. Therefore, an evaluationfunction for second readjustment whose costs are increased with increasein the movement of both the CMY vector Spn+1 and the ink quantity vectorIpn+1 is considered.

[0248] More specifically, the processing is carried out in accordancewith the flowchart in FIG. 9. FIG. 9 is a flowchart illustrating indetail the processing carried out at Step 140 in FIG. 5. In thisembodiment, the evaluation function for first readjustment is given asFormula (36) below.

[0249] [Expression 25]

Eb _(p) =|Ic _(p) ^(n+1) −I _(p) ^(n+1)|²  (36)

[0250] where, the ink quantity vector Icpn+1 is a vector afterreadjustment; and the ink quantity vector Ipn+1 is a vector beforereadjustment, that is, the ink quantity vector calculated at Step 130.

[0251] When print operation is performed with a printer l7 b, ingeneral, there is limitation on the quantity of ink injectable per unitarea in a printing medium. Further, limitation is imposed to prevent theuse of inks of specific color components for specific colors.Consequently, in the minimization, binding conditions wherein theselimitations are formulated can be imposed. Thereby, an ink quantityvector wherein the limitation on ink quantity is met and further theabove lattice point positions are optimized can be determined.

[0252] In this embodiment, these limitations on ink quantity and abinding condition by the above-mentioned matrix K are imposed. Theseconditions are expressed by Formulas (37) to (39) below.

[0253] [Expression 26] $\begin{matrix}{{K \cdot {Ic}_{p}^{n + 1}} = S_{p}^{n + 1}} & (37) \\{{\sum\limits_{m = 1}^{M}\quad {{wd}_{lm} \cdot {ic}_{mp}^{n + 1}}} \leqq d_{l}} & (38)\end{matrix}$

 wo _(m) ·ic _(mp) ^(n+1)=0  (39)

[0254] where, icmpn+1 is each component of the ink quantity vectorIcpn+1; and wdlm is a coefficient for calculating the total value of inkquantities with respect to an arbitrary combination of the ink quantitycomponents, which can take 1 or 0. dl represents the ink quantitylimitation value, which is the maximum value of the total value ofcombined ink quantity components. L is the number of conditions of inkquantity limitation values, and l is the condition number therefor. Thatis, Formula (38) is a formulated ink quantity limitation. Formula (39)is a formulated limitation for preventing use of inks of specific colorcomponents for specific colors. wom is a coefficient which can take 1 ifa specific ink quantity component is not used at some lattice point and0 in any other case. That is, this formula indicates conditions forcases where the existence of a specific ink is not permitted at alattice point indicated by a combination of ink quantity components icmpn+1 (cases where the specific ink quantity component must not haveany value other than 0). m is the component number of ink quantityvector, and in this embodiment, m=1, 2, . . . 6.

[0255] At Step 142, Formula (36) above is minimized with Formulas (37)to (39) above taken as binding conditions. In this embodiment, atechnique designated as quadratic programming is adopted. At this time,to incorporate the inequality indicated as Formula (38) in the bindingconditions, a non-negative artificial variable iul is considered, andFormula (38) is transformed into Formula (40).

[0256] [Expression 27] $\begin{matrix}{{( {\sum\limits_{m = 1}^{M}\quad {{wd}_{lm} \cdot {ic}_{mp}^{n + 1}}} ) + {iu}_{l}} = d_{l}} & (40)\end{matrix}$

[0257] Then, Formulas (37), (39), and (40) representing the bindingconditions are expressed in one formula as Formula (41).

[0258] [Expression 28] $\begin{matrix}{{{A \cdot {Ix}} = B}{A = \begin{pmatrix}\quad & K & \quad & 0_{3L} \\{wd}_{11} & \ldots & {wd}_{1M} & \quad \\\quad & \vdots & \quad & \quad \\\vdots & {wd}_{IM} & \vdots & U_{L} \\\quad & \vdots & \quad & \quad \\{wd}_{L1} & \ldots & {wd}_{LM} & \quad \\{wo}_{1} & \ldots & 0 & \quad \\\quad & \vdots & \quad & \quad \\\vdots & {wo}_{m} & \vdots & 0_{ML} \\\quad & \vdots & \quad & \quad \\0 & \ldots & {wo}_{M} & \quad\end{pmatrix}}{{Ix} = ( {{\begin{matrix}{Ic}_{p}^{n + 1} & {iu}_{1} & \ldots & {iu}_{1} & \ldots &  {iu}_{L} )^{t}\end{matrix}B} = ( \begin{matrix}S_{p}^{n + 1} & d_{1} & \ldots & d_{1} & \ldots & d_{L} & 0 & \ldots &  0 )^{t}\end{matrix} } }} & (41)\end{matrix}$

 Ix=(Ic _(p) ^(n+1) iu ₁ . . . iu ₁ . . . iu _(L))^(t)

B=(S _(p) ^(n+1) d ₁ . . . d ₁ . . . d _(L)0 . . . 0)^(t)

[0259] The matrix A is a matrix with (3+L+M) rows and (M+L) columns, andin this embodiment, the number of inks is 6. Therefore, the 3 rows and Mcolumns at the upper left correspond to the above-mentioned matrix Kwith 3 rows and 6 columns for transforming the 6 component values of inkquantity into 3 component values of CMY lattice point, and 3 rows and Lcolumns at the upper right are a zero matrix. The L rows and M columnsat the middle left are a matrix whose components are the above mentionedcoefficient wdlm. UL at the middle right are a unit matrix with L rowsand L columns. The M rows and M columns at the lower left are a diagonalmatrix whose diagonal components are the coefficient wom. 0 ML at thelower left is a zero matrix with M rows and L columns. The vector Ix isa vector whose components are the ink quantity vector Icpn+1 and theartificial variable iul. The vector B is a vector whose components arethe CMY vector Spn+1, the ink quantity limitation value dl, and 0.

[0260] Therefore, it turns out that Formulas (37), (39), and (40) whichare binding conditions in this embodiment are formulated as one formulaby Formula (41) above. As mentioned above, the evaluation function forfirst readjustment is given by Formula (36) above. Therefore,substituting the ink quantity vector Icpn+1 and the ink quantity vectorIpn+1 in the formula with a vector with the binding conditions takeninto account and minimizing the formula are considered. That is, if theink quantity vector Icpn+1 and the ink quantity vector Ipn+1 in Formula(36) are substituted with vector Ix and vector Iy (Formula (42)), theformula can be expanded as follows:

[0261] [Expression 29]

Iy=(I _(p) ^(n+1)0 . . . 0)  (42)

[0262] [Expression 30] $\begin{matrix}\begin{matrix}{{Eb}_{p} = | {{Ix} - {Iy}} |^{2}} \\{= {{{Ix}^{t} \cdot {Ix}} - {2{{Iy}^{t} \cdot {Ix}}} + {{Iy}^{t} \cdot {Iy}}}} \\{= {d + {C^{t} \cdot {Ix}} + {\frac{1}{2}{{Ix}^{t} \cdot Q \cdot {Ix}}}}}\end{matrix} & (43)\end{matrix}$

[0263] where, d=Iyt·Iy; C=−2 Iy; and Q=2U (U is a unit matrix with (M+L)rows and (M+L) columns).

[0264] That is, in quadratic programming according to this embodiment,Formula (43) only has to be capable of being minimized with Formula (41)taken as a binding condition. When a specific formula is minimized undera specific condition, Lagrange's method of undetermined multipliers canbe utilized. The general-purpose function Fin Lagrange's method ofundetermined multipliers can be expressed by Formula (44) below.

[0265] [Expression 31] $\begin{matrix}\begin{matrix}{{F( {{Ix},{Ra}} )} = {{Eb}_{p} + {{Ra}^{t} \cdot ( {{A \cdot {Ix}} - B} )}}} \\{= {d + {C^{t} \cdot {Ix}} + {\frac{1}{2}{{Ix}^{t} \cdot Q \cdot {Ix}}} + {{Ra}^{t} \cdot ( {{A \cdot {Ix}} - B} )}}}\end{matrix} & (44)\end{matrix}$

[0266] In Formula (44), vector Ra is a Lagrange's undeterminedmultiplier vector, which is a column vector with (3+L+M) columns. If avector Ix which gives the minimal value of the general-purpose functionF exists, the vector Ra is a basic variable vector.

[0267] Further, a column vector Mu with a (M+L) columns indicated inFormula (45) is brought in. Since Formula (45) is 0, Formula (45) issubtracted from Formula (44) to obtain Formula (46), and this Formula(46) is minimized.

[0268] [Expression 32]

MU ^(t) ·Ix0  (45) $\begin{matrix}\begin{matrix}{{F( {{Ix},{Ra}} )} = {d + {C^{t} \cdot {Ix}} + {\frac{1}{2}{{Ix}^{t} \cdot Q \cdot {Ix}}} + {{Ra}^{t} \cdot}}} \\{{( {{A \cdot {Ix}} - B} ) - {{Mu}^{t} \cdot {Ix}}}}\end{matrix} & (46)\end{matrix}$

[0269] In Formula (45), vector Mu is an artificial variable vector. Thecomponents thereof are so constituted that, if either is a basicvariable with respect to components to which the vector Ix corresponds,the other is a non-basic variable. Hence, Formula (45) above is zeroed.

[0270] Here, the general-purpose function F is partially differentiatedwith the components of the vector Ix is made a zero vector as in Formula(47) below. Then, the vector Ix at this time is determined. Thus, thevector Ix when the general-purpose function F is minimized can beobtained.

[0271] [Expression 33] $\begin{matrix}\begin{matrix}{{\frac{\partial}{\partial{ix}_{nt}}{F( {{Ix},{Ra}} )}} = {C + {Q \cdot {Ix}} + {A^{t} \cdot {Ra}} - {Mu}}} \\{= 0_{Nt}}\end{matrix} & (47)\end{matrix}$

[0272] In Formula (47), ixnt represents a component of vector I x; nt(=1 to (M+L)) is a component number of vector Ix. 0 Nt is a zero vectorwith (M+L) columns. If an optimal solution which minimizes Formula (46)exists, then vector Ix which satisfies all of Formulas (41), (47), and(45) above exists. As a concrete solution for calculating the vector Ix,the simplex first-stage solution, which is widely known with respect tolinear programming, or the like can be adopted. Needless to add, inaddition to quadratic programming, various solutions, includingpseudo-Newton method, can be adopted for minimizing Formula (36) above.

[0273] As mentioned above, at Step 142, the optimal solution is computedto calculate the ink quantity vector Icpn+1. Under some conditions,Formula (37) and Formula (38) or (39) are not compatible with eachother. Consequently, at Step 144, it is judged whether the ink quantityvector Icpn+1 was calculated at Step 142. If it is judged at Step 144that the ink quantity vector Icpn+1 was calculated, at Step 148, the inkquantity vector Icpn+1 is substituted into the ink quantity vectorIpn+1. Thus, the result is taken as an ink quantity vector value afterreadjustment.

[0274] If it is not judged at Step 144 that the ink quantity vectorIcpn+1 was calculated, at Steps 146 and 147, the movement of CMY latticepoints is permitted. Further, the ink quantity vector and the CMY vectorare readjusted with the limitations on ink quantity taken into account.In this embodiment, the movement of CMY lattice points is reduced asmuch as possible. Therefore, Formula (48) below is adopted as theevaluation function for second readjustment.

[0275] [Expression 34]

Ec _(p) =|Wci·(Ic _(p) ^(n+1) −I _(p) ^(n+1))|² +|Wcs·(K·Ic _(p) ^(n+1)−S _(p) ^(n+1))|²  (48)

[0276] Here, Wci is a diagonal matrix with M rows and M columns, andeach component is a weighting matrix representing the weight for eachink quantity component. Wcs is a diagonal matrix with 3 rows and 3columns, and each component is a weighting matrix representing theweight for each CMY component. By adjusting the value of each weightingmatrix, the movement of CMY lattice points and ink quantity latticepoints can be adjusted relative to each other. For example, it may bedesired to make the movement of CMY lattice points smaller than themovement of ink quantity lattice points. In this case, a weightingfactor can be determined under such a condition as Formula (49) belowwith respect to arbitrary m and q.

wcim<<wcsq  (49)

[0277] where, wcim is a diagonal component of the matrix Wci; and wcsqis a diagonal component of the matrix Wcs.

[0278] The weighting factor wcsq is so set that the value thereof willbe increased as the values of the components of the CMY vector arereduced. For example, the cyan component and the magenta component ofCMY vector Spn+1 are compared with each other. If the value of the cyancomponent is larger than that of the magenta component, the weightingfactor is determined as indicated in Formula (50) below.

wcsc≦wcsm  (50)

[0279] More specific description will be given. A smaller componentvalue of CMY vector is more largely influenced by a certain amount ofvariation than a larger component value is. Therefore, the magnitude ofinverse number order is given to the weighting factor, and theinfluences are thereby lessened (averaged).

[0280] At Step 146, the weighting matrix Wcs is calculated from eachcomponent value of CMY vector Spn+1, as mentioned above. Further, thematrix Wci is computed to determine the evaluation function Ecp forsecond readjustment shown in Formula (48). At Step l47, the optimalsolution which minimizes the evaluation function Ecp for secondreadjustment shown in Formula (48), and thereby the ink quantity vectorIcpn+1 when Ecp is minimized is calculated. At this time, by utilizingquadratic programming, which was utilized to minimize the evaluationfunction for first readjustment, the optimal solution can be computed.As binding conditions, Formulas (38) and (39) are utilized. The concretesolving method is in accordance with the solving method for minimizingthe evaluation function for first readjustment.

[0281] After the ink quantity vector Icpn+1 is calculated as mentionedabove, the ink quantity vector Icpn+1 is substituted into the inkquantity vector Ipn+1 at Step 148. Further, the CMY vector Spn+1calculated at Step 102 to Step 116 is updated with the ink quantityvector Ipn+1 and Formula (1) above. As a result, lattice points whichare CMY lattice points and ink quantity lattice points readjusted withrespect to a lattice of number p and in correspondence with each othercan be determined.

[0282] (8) Other Embodiments:

[0283] In the above embodiment, the correspondence definition data is acolor correction LUT. The color correction LUT is generated bysubjecting print colors, specified by lattice points for correspondencedefinition data creation determined by a method according to the presentinvention, to color measuring. Needless to add, the embodiment of thepresent invention is not limited to this. For example, correspondencedefinition data may be a profile, and the profile may be generated bysubjecting print colors, specified by lattice points for correspondencedefinition data creation determined by a method according to the presentinvention, to color measuring.

[0284] This embodiment is implemented by constituting a profilegenerating portion which is capable of generating profiles in the colorcorrection LUT generator 20A illustrated in FIG. 1, instead of the colorcorrection LUT generating portion 20 i; and by constituting a profilestoring portion, instead of the color correction LUT storing portion 20b. In this case, the profile generating portion generates profiles fromcolor measuring data acquired by the color measuring data acquiringportion 20 h, and the generated profiles are stored in the profilestoring portion.

[0285] More specifically, a print patch wherein the components ofCMYKlclm image data are the color components of ink quantity latticepoints generated at the portion 20 g for generating LUT before colormatching is printed. Then, the color measuring data acquiring portion 20h acquires color measuring data obtained from color measuring by a colormeasuring instrument or the like. As a result, colors indicated by theink quantity lattice points can be rendered in non-equipment dependentcolors. Therefore, various types of profile can be generated. Suchprofiles include a profile wherein colors indicated by ink quantitylattice points are in correspondence with the above-mentioned sRGB imagedata; and a profile wherein colors indicated by ink quantity latticepoints are in correspondence with coordinate data on coordinates in theLab color space. These profiles are generated at the above-mentionedprofile generating portion.

[0286] The profile only has to be capable of bringing image data whichspecifies colors in a specific color space into correspondence withCMYKlclm image data, and various modes can be adopted therefor. Morespecifically, it may be LUT which defines one-to-one color relation withrespect to a plurality of representative points. Or, it may be a profilewhich defines color relation by specific functions, matrices, or thelike. Alternatively, a profile may be generated in accordance with theICC (International Color Consortium) standard. Needless to add, in thiscase as well, the present invention holds in a profile generator, aprofile generating method, a profile generating program, and a recordingmedium therefor.

We claim
 1. A lattice point determining method for correspondencedefinition data creation, whereby a plurality of lattice points whichare referred to when correspondence definition data which definescorrespondence between the ink quantities of inks in more than 3, CMY,colors used in a printing device and the color component values ofvarious colors used in another image device is created are determined,the method comprising: a step of defining both an ink quantity latticepoint smoothness evaluation function for evaluating the smoothness ofthe disposition of ink quantity lattice points whose components are saidink quantities of inks in various colors and a CMY lattice pointsmoothness evaluation function for evaluating the smoothness of thedisposition of CMY lattice points defined by CMY color components; and astep of taking both CMY lattice points and ink quantity lattice pointswherein said ink quantity lattice point smoothness evaluation functionand said CMY lattice point smoothness evaluation function are separatelysubstantially minimized, as lattice points for correspondence definitiondata creation.
 2. The lattice point determining method forcorrespondence definition data creation, whereby a plurality of latticepoints which are referred to when correspondence definition data whichdefines correspondence between the ink quantities of inks in variouscolors used in a printing device and the color component values ofvarious colors used in another image device is created are determined,the method comprising: a step of defining both an ink quantity latticepoint smoothness evaluation function for evaluating the smoothness ofthe disposition of ink quantity lattice points in an ink quantity spacewhose components are said ink quantities of inks in various colors and alower-dimensional color lattice point smoothness evaluation function forevaluating the smoothness of the disposition of lower-dimensional colorlattice points in a lower-dimensional color space defined by a smallernumber of color components than the number of these inks; a step ofseparately optimizing the ink quantity lattice points and thelower-dimensional color lattice points by separately enhancing theevaluations of said ink quantity lattice point smoothness evaluationfunction and said lower-dimensional color lattice point smoothnessevaluation function; and a step of determining a plurality of saidlattice points by keeping either of the ink quantity lattice points andthe lower-dimensional color lattice points at the optimized latticepoints and readjusting the other optimized lattice points.
 3. Thelattice point determining method for correspondence definition datacreation, according to claim 2, wherein: either or both of the inkquantity lattice point smoothness evaluation function and thelower-dimensional color lattice point smoothness evaluation functioncontain a function whose value is increased with increase in thedifference between the relative positional relation between a latticepoint of interest and a lattice point adjacent thereto and the relativepositional relation between a comparative lattice point adjacent to saidlattice point of interest and a lattice point adjacent thereto.
 4. Thelattice point determining method for correspondence definition datacreation, according to claim 3, wherein: the difference in said relativepositional relation contains a function which contains as a component avalue obtained by dividing the differential vector between a vectorconnecting said lattice point of interest and a lattice point adjacentthereto and a vector connecting a comparative lattice point adjacent tosaid lattice point of interest and a lattice point adjacent thereto bythe distance between said lattice point of interest and said comparativelattice point.
 5. The lattice point determining method forcorrespondence definition data creation, according to claim 2, wherein:either or both of said ink quantity lattice point smoothness evaluationfunction and the lower-dimensional color lattice point smoothnessevaluation function contain a function whose value is increased as alattice point of interest gets away from a specific position.
 6. Thelattice point determining method for correspondence definition datacreation, according to claim 2, wherein: either or both of said inkquantity lattice point smoothness evaluation function and saidlower-dimensional color lattice point smoothness evaluation functioncontain a function whose value is increased as a color indicated by alattice point of interest deviates from a specific color.
 7. The latticepoint determining method for correspondence definition data creation,according to claim 2, wherein: either or both of said ink quantitylattice point smoothness evaluation function and said lower-dimensionalcolor lattice point smoothness evaluation function are functions whichcontain as variables color components constituting respective colorspaces; and a deviation which is added to the color components of alattice point when the evaluation functions are minimized inoptimization with respect to the lattice point is calculated and thelattice point is repeatedly corrected by an amount equivalent to thedeviation to enhance the evaluation of the smoothness of thedisposition.
 8. The lattice point determining method for correspondencedefinition data creation, according to claim 2, wherein: in readjustmentof said ink quantity lattice points, binding conditions are imposed sothat the ink quantity lattice points after readjustment will betransformed into said optimized low-dimensional color lattice points bya predetermined transformation expression for transforming ink quantitylattice points into lower-dimensional color lattice points, and therebythe ink quantity lattice points are determined.
 9. A lattice pointdetermining method for correspondence definition data creation whereby aplurality of lattice points which are referred to when correspondencedefinition data which defines correspondence between the ink quantitiesof inks in more than 3, CMY, colors used in a printing device and thecolor component values of various colors used in another image deviceare determined, the method comprising: a step of defining both an inkquantity lattice point smoothness evaluation function for evaluating thesmoothness of the disposition of ink quantity lattice points whosecomponents are said ink quantities of inks in various colors and a CMYlattice point smoothness evaluation function for evaluating thesmoothness of the disposition of CMY lattice points defined by CMY colorcomponents; a step of separately minimizing said ink quantity latticepoint smoothness evaluation function and said CMY lattice pointsmoothness evaluation function; a step of imposing binding conditions sothat the ink quantity lattice points after readjustment will betransformed into CMY color lattice points determined by saidminimization, by a predetermined transformation expression fortransforming ink quantity lattice points into CMY lattice points; a stepof imposing limitation on ink quantity adhering to a printing medium asa binding condition when the ink quantity lattice points and the CMYlattice points are brought into correspondence with each other; and astep of taking both the CMY lattice points determined by readjusting inkquantity lattice point positions and the ink quantity lattice points, aslattice points for correspondence definition data creation.
 10. Alattice point determining method for correspondence definition datacreation whereby a plurality of lattice points which are referred towhen correspondence definition data which defines correspondence betweenthe ink quantities of inks in various colors used in a printing deviceand the color component values of various colors used in another imagedevice is created are determined, the method comprising: a step ofdefining both an ink quantity lattice point smoothness evaluationfunction for evaluating the smoothness of disposition of ink quantitylattice points in an ink quantity space whose components are said colorink quantities of inks in various colors and a lower-dimensional colorlattice point smoothness evaluation function for evaluating thesmoothness of the disposition of lower-dimensional color lattice pointsin a lower-dimensional color space defined by a smaller number of colorcomponents than the number of these inks; a step of separatelyoptimizing the ink quantity lattice points and the lower-dimensionalcolor lattice points by separately enhancing the evaluations of said inkquantity lattice point smoothness evaluation function and saidlower-dimensional color lattice point smoothness evaluation function; astep of maintaining either of the ink quantity lattice points and thelower-dimensional color lattice points at optimized lattice points andreadjusting the other optimized lattice points; and a step of imposinglimitation on ink quantity caused to adhere to a printing medium as abinding condition when a plurality of said lattice points are determinedby said step of maintaining and readjusting, and carrying out saidreadjustment.
 11. The lattice point determining method forcorrespondence definition data creation, according to claim 10, wherein:said readjustment is made by minimizing a first movement evaluationfunction containing a function whose value is increased with increase inthe distance between the lattice points after readjustment and saidother optimized lattice points.
 12. The lattice point determining methodfor correspondence definition data creation, according to claim 10,wherein: said limitation on ink quantity is limitation on the maximumquantity of ink adhering to a specific printing area.
 13. The latticepoint determining method for correspondence definition data creation,according to claim 12, wherein: said maximum quantity of ink adhering iscalculated by adding up the product of a weighting factor whose value is“0” or “1” defined for each ink quantity component value and eachcomponent value of said ink quantity lattice points.
 14. The latticepoint determining method for correspondence definition data creation,according to claim 10, wherein: said limitation on ink quantity islimitation on the quantity of a specific color ink consumed at aspecific gradation value.
 15. The lattice point determining method forcorrespondence definition data creation, according to claim 14, wherein:said limitation on the quantity of a specific color ink consumed isdefined by a condition that the product of a weighting factor whosevalue is “0” or “1” defined for each ink quantity component value andeach component value of said ink quantity lattice points is “0.”
 16. Thelattice point determining method for correspondence definition datacreation, according to claim 11, wherein: if there is not a solutionwhich minimizes said first movement evaluation function when thepositions of said either optimized lattice points in said readjustment,it is permitted to fluctuate the positions of said either optimizedlattice points and said readjustment is made by minimizing a secondmovement evaluation function containing a function whose value isincreased with increase in the distance between the lattice points afterreadjustment and said other optimized lattice points and furtherincreased with increase in the moving distance of said either optimizedlattice points.
 17. The lattice point determining method forcorrespondence definition data creation, according to claim 16, wherein:in said second movement evaluation function, the unit fluctuation ofsaid either optimized lattice points more greatly contributes toincrease in the value of the second movement evaluation function thanthe unit fluctuation of said other optimized lattice points.
 18. Thelattice point determining method for correspondence definition datacreation, according to claim 16, wherein: in said second movementevaluation function, the unit fluctuation of components having a smallabsolute value of said either optimized lattice points more greatlycontributes to increase in the value of the second movement evaluationfunction than the unit fluctuation of components having a large absolutevalue in comparison.
 19. An image processor which refers tocorrespondence definition data which defines correspondence between theink quantities of inks in various colors used in a printing device andthe color component values of various colors used in another imagedevice and generates print data for converting the color componentvalues of various colors used in said image device into said inkquantities to cause print operation to be performed, wherein: saidcorrespondence definition data is data created by defining an inkquantity lattice point smoothness evaluation function for evaluating thesmoothness of the disposition of ink quantity lattice points in an inkquantity space whose components are said ink quantities of inks invarious colors and a lower-dimensional color lattice point smoothnessevaluation function for evaluating the smoothness of the disposition oflower-dimensional color lattice points in a lower-dimensional colorspace which is defined by a smaller number of color components than thenumber of these inks; separately enhancing the evaluations of said inkquantity lattice point smoothness evaluation function and saidlower-dimensional color lattice point smoothness evaluation function toseparately optimize the ink quantity lattice points and thelower-dimensional color lattice points; keeping either of the inkquantity lattice points and the lower-dimensional color lattice pointsat optimized lattice points and readjusting the other optimized latticepoints to determine a plurality of lattice points as lattice points forcorrespondence definition data creation; and bringing said inkquantities and the color component values of various colors used in saidanother image device into correspondence with each other by colormeasuring values obtained by subjecting the result of printing with inkquantities defined by the lattice points for correspondence definitiondata creation to color measuring with a predetermined color measuringinstrument.
 20. An image processing method wherein correspondencedefinition data which defines correspondence between the ink quantitiesof inks in various colors used in a printing device and the colorcomponent values of various colors used in another image device isreferred to and thereby print data for converting the color componentvalue of various colors used in said image device into said inkquantities to cause print operation to be performed is created, wherein:said correspondence definition data is data created by defining an inkquantity lattice point smoothness evaluation function for evaluating thesmoothness of the disposition of ink quantity lattice points in an inkquantity space whose components are said ink quantities of inks invarious colors and a lower-dimensional color lattice point smoothnessevaluation function for evaluating the smoothness of the disposition oflower-dimensional color lattice points in a lower-dimensional colorspace defined by a smaller number of color components than the number ofthese inks; separately enhancing the evaluations of said ink quantitylattice point smoothness evaluation function and said lower-dimensionalcolor lattice point smoothness evaluation function to separatelyoptimize the ink quantity lattice points and the lower-dimensional colorlattice points; keeping either of the ink quantity lattice points andthe lower-dimensional color lattice points at optimized lattice pointsand readjusting the other optimized lattice points to determine aplurality of lattice points as lattice points for correspondencedefinition data creation; and bringing said ink quantities and the colorcomponent values of various colors used in said another image deviceinto correspondence with each other by color measuring values obtainedby subjecting the result of printing with ink quantities defined by thelattice points for correspondence definition data creation to colormeasuring with a predetermined color measuring instrument.
 21. A mediumwith an image processing program recorded thereon which program is forcausing a computer to carry out a function of referring tocorrespondence definition data which defines correspondence between theink quantities of inks in various colors used in a printing device andthe color component values of various colors used in another imagedevice and creating print data for converting the color component valuesof various color used in said image device into said ink quantities tocause print operation to be performed, wherein: said correspondencedefinition data is data created by defining an ink quantity latticepoint smoothness evaluation function for evaluating the smoothness ofthe disposition of ink quantity lattice points in an ink quantity spacewhose components are said ink quantities of inks in various colors and alower-dimensional color lattice point smoothness evaluation function forevaluating the smoothness of the disposition of lower-dimensional colorlattice points in a lower-dimensional color space defined by a smallernumber of color components than the number of these inks; separatelyenhancing the evaluations of said ink quantity lattice point smoothnessevaluation function and said lower-dimensional color lattice pointsmoothness evaluation function to separately optimize the ink quantitylattice points and the lower-dimensional color lattice points; keepingeither of the ink quantity lattice points and the lower-dimensionalcolor lattice points at optimized lattice points and readjusting theother optimized lattice points to determine a plurality of latticepoints as lattice points for correspondence definition data creation;and bringing said ink quantities and the color component values ofvarious colors used in said another image device into correspondencewith each other by color measuring values obtained by subjecting theresult of printing with ink quantities defined by the lattice points forcorrespondence definition data creation to color measuring with apredetermined color measuring instrument.
 22. An image processor whichrefers to correspondence definition data which defines correspondencebetween the ink quantities of inks in various colors used in a printingdevice and the color component values of various colors used in anotherimage device and creates print data for converting the color componentvalues of various colors used in said image device into said inkquantities to cause print operation to be performed, wherein: saidcorrespondence definition data is data created by defining an inkquantity lattice point smoothness evaluation function for evaluating thesmoothness of the disposition of ink quantity lattice points in an inkquantity space whose components are said ink quantities of inks invarious colors and a lower-dimensional color lattice point smoothnessevaluation function for evaluating the smoothness of the disposition oflower-dimensional color lattice points in a lower-dimensional colorspace defined by a smaller number of color components than the number ofthese inks; separately enhancing the evaluations of said ink quantitylattice point smoothness evaluation function and said lower-dimensionalcolor lattice point smoothness evaluation function to separatelyoptimize the ink quantity lattice points and the lower-dimensional colorlattice points; keeping either of the ink quantity lattice points andthe lower-dimensional color lattice points at optimized lattice pointsand readjusting the other optimized lattice points to determine aplurality of said lattice points; imposing limitation on ink quantitiesadhering to a printing medium as a binding condition in saidreadjustment to determine a plurality of the lattice points as latticepoints for correspondence definition data creation; and bringing saidink quantities and the color component values of various colors used insaid another image device into correspondence with each other by colormeasuring values obtained by subjecting the result of printing with inkquantities defined by the lattice points for correspondence definitiondata creation to color measuring with a predetermined color measuringinstrument.
 23. An image processing method wherein correspondencedefinition data which defines correspondence between the ink quantitiesof inks in various colors used in a printing device and the colorcomponent values of various colors used in another image device isreferred to and print data for converting the color component values ofcolors used in said image device into said ink quantities to cause printoperation to be performed is created, wherein: said correspondencedefinition data is data created by defining an ink quantity latticepoint smoothness evaluation function for evaluating the smoothness ofthe disposition of ink quantity lattice points in an ink quantity spacewhose components are said ink quantities of inks in various colors and alower-dimensional color lattice point smoothness evaluation function forevaluating the smoothness of the disposition of lower-dimensional colorlattice points in a lower-dimensional color space defined by a smallernumber of color components than the number of these inks; separatelyenhancing the evaluations of said ink quantity lattice point smoothnessevaluation functions and said lower-dimensional color lattice pointsmoothness evaluation function to separately optimize the ink quantitylattice points and the lower-dimensional color lattice points; keepingeither of the ink quantity lattice points and the lower-dimensionalcolor lattice points at optimized lattice points and readjusting theother optimized lattice points to determine a plurality of said latticepoints; imposing limitation on ink quantities adhering to a printingmedium as a binding condition in said readjustment to determine aplurality of the lattice points as lattice points for correspondencedefinition data creation; and bringing said ink quantities and the colorcomponent values of various colors used in said image device intocorrespondence with each other by color measuring values obtained bysubjecting the result of printing with ink quantities defined by thelattice points for correspondence definition data creation to colormeasuring with a predetermined color measuring instrument.
 24. A mediumwith an image processing program recorded thereon which program is forcausing a computer to carry out a function of referring tocorrespondence definition data which defines correspondence between theink quantities of inks in various colors used in a printing device andthe color component values of various colors used in another imagedevice and creating print data for converting the color component valuesof various colors used in said image device into said ink quantities tocause print operation to be performed, wherein: said correspondencedefinition data is data created by defining an ink quantity latticepoint smoothness evaluation function for evaluating the smoothness ofthe disposition of ink quantity lattice points in an ink quantity spacewhose components are said ink quantities of inks in various colors and alower-dimensional color lattice point smoothness evaluation function forevaluating the smoothness of the disposition of lower-dimensional colorlattice points in a lower-dimensional color space defined by a smallernumber of color components than the number of these inks; separatelyenhancing the evaluations of said ink quantity lattice point smoothnessevaluation function and said lower-dimensional color lattice pointsmoothness evaluation function to separately optimize the ink quantitylattice points and the lower-dimensional color lattice points; keepingeither of the ink quantity lattice points and the lower-dimensionalcolor lattice points at optimized lattice points and readjusting theother optimized lattice points to determine a plurality of latticepoints; imposing limitation on ink quantities adhering to a printingmedium as a binding condition in said readjustment to determine aplurality of the lattice points as lattice points for correspondencedefinition data creation; and bringing said ink quantities and the colorcomponent values of various colors used in said another image deviceinto correspondence with each other by color measuring values obtainedby subjecting the result of printing with ink quantities defined by thelattice points for correspondence definition data creation to colormeasuring with a predetermined color measuring instrument.